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Determinante ist genau dann ungleich ",[572,3123,3125,3138],{"className":3124},[575],[572,3126,3128],{"className":3127},[579],[581,3129,3130],{"xmlns":583},[585,3131,3132,3136],{},[588,3133,3134],{},[591,3135,697],{},[601,3137,697],{"encoding":603},[572,3139,3141],{"className":3140,"ariaHidden":609},[608],[572,3142,3144,3147],{"className":3143},[613],[572,3145],{"className":3146,"style":641},[617],[572,3148,697],{"className":3149},[622],", wenn ",[572,3152,3154,3167],{"className":3153},[575],[572,3155,3157],{"className":3156},[579],[581,3158,3159],{"xmlns":583},[585,3160,3161,3165],{},[588,3162,3163],{},[703,3164,1851],{},[601,3166,1851],{"encoding":603},[572,3168,3170],{"className":3169,"ariaHidden":609},[608],[572,3171,3173,3177],{"className":3172},[613],[572,3174],{"className":3175,"style":3176},[617],"height:0.6833em;",[572,3178,1851],{"className":3179},[622,920]," invertierbar ist, also wenn die Spalten linear unabhängig sind. Ihr Betrag ist das Volumen des Spats, den die Spalten (oder Zeilen) aufspannen. Für Dreiecksmatrizen ist sie das Produkt der Diagonaleinträge.",[559,3182,3184],{"id":3183},"beispiele","Beispiele",[572,3186,3188],{"className":3187},[669],[572,3189,3191,3382],{"className":3190},[575],[572,3192,3194],{"className":3193},[579],[581,3195,3196],{"xmlns":583,"display":678},[585,3197,3198,3379],{},[588,3199,3200,3202,3204,3276,3278,3280,3283,3285,3287,3289,3291,3293,3295,3297,3299,3301,3303,3305,3307,3309,3311,3313,3315,3317,3319,3321,3323,3325,3327,3329,3331,3333,3335,3337,3339,3341,3343,3345,3347,3349,3351,3354,3356,3358,3360,3362,3364,3366,3368,3370,3372,3374,3376],{},[703,3201,1845],{},[595,3203,1848],{},[588,3205,3206,3208,3274],{},[595,3207,1869],{"fence":609},[682,3209,3211,3233,3253],{"rowspacing":684,"columnalign":3210,"columnspacing":687},"center center 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18",[572,3383,3385,3681,3699,3717,3735,3753,3771,3789,3807,3825,3843,3861,3879,3897,3915,3933,3951,3969,3987,4005,4023,4041,4059,4077,4095,4113],{"className":3384,"ariaHidden":609},[608],[572,3386,3388,3391,3394,3397,3672,3675,3678],{"className":3387},[613],[572,3389],{"className":3390,"style":873},[617],[572,3392,1845],{"className":3393},[2066],[572,3395],{"className":3396,"style":2070},[626],[572,3398,3400,3448,3634],{"className":3399},[2147],[572,3401,3403],{"className":3402},[2151],[572,3404,3407],{"className":3405},[2157,3406],"mult",[572,3408,3410,3440],{"className":3409},[892,893],[572,3411,3413,3437],{"className":3412},[897],[572,3414,3416],{"className":3415,"style":902},[901],[572,3417,3419,3423],{"style":3418},"top:-4.05em;",[572,3420],{"className":3421,"style":3422},[909],"height:5.6em;",[572,3424,3426],{"style":3425},"width:0.875em;height:3.6em;",[3427,3428,3433],"svg",{"xmlns":3429,"width":3430,"height":3431,"viewBox":3432},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.875em","3.6em","0 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Zeile:",[572,4126,4128],{"className":4127},[669],[572,4129,4131,4206],{"className":4130},[575],[572,4132,4134],{"className":4133},[579],[581,4135,4136],{"xmlns":583,"display":678},[585,4137,4138,4203],{},[588,4139,4140,4142,4144,4146,4148,4150,4152,4154,4156,4158,4160,4162,4164,4166,4168,4170,4172,4174,4176,4178,4180,4182,4184,4186,4188,4191,4193,4195,4197,4199,4201],{},[591,4141,3219],{},[595,4143,3282],{},[595,4145,1869],{"stretchy":698},[591,4147,719],{},[595,4149,1922],{},[591,4151,3219],{},[595,4153,1919],{"stretchy":698},[595,4155,1922],{},[591,4157,697],{},[595,4159,3282],{},[595,4161,1869],{"stretchy":698},[591,4163,3273],{},[595,4165,1922],{},[591,4167,3219],{},[595,4169,1919],{"stretchy":698},[595,4171,1987],{},[591,4173,3232],{},[595,4175,3282],{},[595,4177,1869],{"stretchy":698},[591,4179,3232],{},[595,4181,1922],{},[591,4183,593],{},[595,4185,1919],{"stretchy":698},[595,4187,1854],{},[591,4189,4190],{},"20",[595,4192,1922],{},[591,4194,697],{},[595,4196,1922],{},[591,4198,3219],{},[595,4200,1854],{},[591,4202,3378],{},[601,4204,4205],{"encoding":603},"2 \\cdot (12 - 2) - 0 \\cdot (4 - 2) + 1 \\cdot (1 - 3) = 20 - 0 - 2 = 18",[572,4207,4209,4227,4249,4270,4288,4309,4330,4348,4369,4390,4408,4426,4444],{"className":4208,"ariaHidden":609},[608],[572,4210,4212,4215,4218,4221,4224],{"className":4211},[613],[572,4213],{"className":4214,"style":641},[617],[572,4216,3219],{"className":4217},[622],[572,4219],{"className":4220,"style":627},[626],[572,4222,3282],{"className":4223},[631],[572,4225],{"className":4226,"style":627},[626],[572,4228,4230,4234,4237,4240,4243,4246],{"className":4229},[613],[572,4231],{"className":4232,"style":4233},[617],"height:1em;vertical-align:-0.25em;",[572,4235,1869],{"className":4236},[2151],[572,4238,719],{"className":4239},[622],[572,4241],{"className":4242,"style":627},[626],[572,4244,1922],{"className":4245},[631],[572,4247],{"className":4248,"style":627},[626],[572,4250,4252,4255,4258,4261,4264,4267],{"className":4251},[613],[572,4253],{"className":4254,"style":4233},[617],[572,4256,3219],{"className":4257},[622],[572,4259,1919],{"className":4260},[2427],[572,4262],{"className":4263,"style":627},[626],[572,4265,1922],{"className":4266},[631],[572,4268],{"className":4269,"style":627},[626],[572,4271,4273,4276,4279,4282,4285],{"className":4272},[613],[572,4274],{"className":4275,"style":641},[617],[572,4277,697],{"className":4278},[622],[572,4280],{"className":4281,"style":627},[626],[572,4283,3282],{"className":4284},[631],[572,4286],{"className":4287,"style":627},[626],[572,4289,4291,4294,4297,4300,4303,4306],{"className":4290},[613],[572,4292],{"className":4293,"style":4233},[617],[572,4295,1869],{"className":4296},[2151],[572,4298,3273],{"className":4299},[622],[572,4301],{"className":4302,"style":627},[626],[572,4304,1922],{"className":4305},[631],[572,4307],{"className":4308,"style":627},[626],[572,4310,4312,4315,4318,4321,4324,4327],{"className":4311},[613],[572,4313],{"className":4314,"style":4233},[617],[572,4316,3219],{"className":4317},[622],[572,4319,1919],{"className":4320},[2427],[572,4322],{"className":4323,"style":627},[626],[572,4325,1987],{"className":4326},[631],[572,4328],{"className":4329,"style":627},[626],[572,4331,4333,4336,4339,4342,4345],{"className":4332},[613],[572,4334],{"className":4335,"style":641},[617],[572,4337,3232],{"className":4338},[622],[572,4340],{"className":4341,"style":627},[626],[572,4343,3282],{"className":4344},[631],[572,4346],{"className":4347,"style":627},[626],[572,4349,4351,4354,4357,4360,4363,4366],{"className":4350},[613],[572,4352],{"className":4353,"style":4233},[617],[572,4355,1869],{"className":4356},[2151],[572,4358,3232],{"className":4359},[622],[572,4361],{"className":4362,"style":627},[626],[572,4364,1922],{"className":4365},[631],[572,4367],{"className":4368,"style":627},[626],[572,4370,4372,4375,4378,4381,4384,4387],{"className":4371},[613],[572,4373],{"className":4374,"style":4233},[617],[572,4376,593],{"className":4377},[622],[572,4379,1919],{"className":4380},[2427],[572,4382],{"className":4383,"style":2077},[626],[572,4385,1854],{"className":4386},[2081],[572,4388],{"className":4389,"style":2077},[626],[572,4391,4393,4396,4399,4402,4405],{"className":4392},[613],[572,4394],{"className":4395,"style":618},[617],[572,4397,4190],{"className":4398},[622],[572,4400],{"className":4401,"style":627},[626],[572,4403,1922],{"className":4404},[631],[572,4406],{"className":4407,"style":627},[626],[572,4409,4411,4414,4417,4420,4423],{"className":4410},[613],[572,4412],{"className":4413,"style":618},[617],[572,4415,697],{"className":4416},[622],[572,4418],{"className":4419,"style":627},[626],[572,4421,1922],{"className":4422},[631],[572,4424],{"className":4425,"style":627},[626],[572,4427,4429,4432,4435,4438,4441],{"className":4428},[613],[572,4430],{"className":4431,"style":641},[617],[572,4433,3219],{"className":4434},[622],[572,4436],{"className":4437,"style":2077},[626],[572,4439,1854],{"className":4440},[2081],[572,4442],{"className":4443,"style":2077},[626],[572,4445,4447,4450],{"className":4446},[613],[572,4448],{"className":4449,"style":641},[617],[572,4451,3378],{"className":4452},[622],[564,4454,4455,4456,4825,4826,659],{},"Für die obere Dreiecksmatrix ",[572,4457,4459,4547],{"className":4458},[575],[572,4460,4462],{"className":4461},[579],[581,4463,4464],{"xmlns":583},[585,4465,4466,4544],{},[588,4467,4468,4470,4542],{},[595,4469,1869],{"fence":609},[682,4471,4472,4497,4518],{"rowspacing":684,"columnalign":3210,"columnspacing":687},[689,4473,4474,4480,4487],{},[692,4475,4476],{},[695,4477,4478],{"scriptlevel":697,"displaystyle":698},[591,4479,3219],{},[692,4481,4482],{},[695,4483,4484],{"scriptlevel":697,"displaystyle":698},[591,4485,4486],{},"5",[692,4488,4489],{},[695,4490,4491],{"scriptlevel":697,"displaystyle":698},[588,4492,4493,4495],{},[595,4494,1922],{},[591,4496,3232],{},[689,4498,4499,4505,4511],{},[692,4500,4501],{},[695,4502,4503],{"scriptlevel":697,"displaystyle":698},[591,4504,697],{},[692,4506,4507],{},[695,4508,4509],{"scriptlevel":697,"displaystyle":698},[591,4510,593],{},[692,4512,4513],{},[695,4514,4515],{"scriptlevel":697,"displaystyle":698},[591,4516,4517],{},"7",[689,4519,4520,4526,4532],{},[692,4521,4522],{},[695,4523,4524],{"scriptlevel":697,"displaystyle":698},[591,4525,697],{},[692,4527,4528],{},[695,4529,4530],{"scriptlevel":697,"displaystyle":698},[591,4531,697],{},[692,4533,4534],{},[695,4535,4536],{"scriptlevel":697,"displaystyle":698},[588,4537,4538,4540],{},[595,4539,1922],{},[591,4541,3273],{},[595,4543,1919],{"fence":609},[601,4545,4546],{"encoding":603},"\\begin{pmatrix} 2 & 5 & -1 \\\\ 0 & 3 & 7 \\\\ 0 & 0 & -4 \\end{pmatrix}",[572,4548,4550],{"className":4549,"ariaHidden":609},[608],[572,4551,4553,4556],{"className":4552},[613],[572,4554],{"className":4555,"style":873},[617],[572,4557,4559,4596,4788],{"className":4558},[2147],[572,4560,4562],{"className":4561},[2151],[572,4563,4565],{"className":4564},[2157,3406],[572,4566,4568,4588],{"className":4567},[892,893],[572,4569,4571,4585],{"className":4570},[897],[572,4572,4574],{"className":4573,"style":902},[901],[572,4575,4576,4579],{"style":3418},[572,4577],{"className":4578,"style":3422},[909],[572,4580,4581],{"style":3425},[3427,4582,4583],{"xmlns":3429,"width":3430,"height":3431,"viewBox":3432},[3434,4584],{"d":3436},[572,4586,959],{"className":4587},[958],[572,4589,4591],{"className":4590},[897],[572,4592,4594],{"className":4593,"style":1082},[901],[572,4595],{},[572,4597,4599],{"className":4598},[622],[572,4600,4602,4658,4661,4664,4720,4723,4726],{"className":4601},[682],[572,4603,4605],{"className":4604},[888],[572,4606,4608,4650],{"className":4607},[892,893],[572,4609,4611,4647],{"className":4610},[897],[572,4612,4614,4625,4636],{"className":4613,"style":902},[901],[572,4615,4616,4619],{"style":905},[572,4617],{"className":4618,"style":910},[909],[572,4620,4622],{"className":4621},[622],[572,4623,3219],{"className":4624},[622],[572,4626,4627,4630],{"style":971},[572,4628],{"className":4629,"style":910},[909],[572,4631,4633],{"className":4632},[622],[572,4634,697],{"className":4635},[622],[572,4637,4638,4641],{"style":1023},[572,4639],{"className":4640,"style":910},[909],[572,4642,4644],{"className":4643},[622],[572,4645,697],{"className":4646},[622],[572,4648,959],{"className":4649},[958],[572,4651,4653],{"className":4652},[897],[572,4654,4656],{"className":4655,"style":1082},[901],[572,4657],{},[572,4659],{"className":4660,"style":884},[883],[572,4662],{"className":4663,"style":884},[883],[572,4665,4667],{"className":4666},[888],[572,4668,4670,4712],{"className":4669},[892,893],[572,4671,4673,4709],{"className":4672},[897],[572,4674,4676,4687,4698],{"className":4675,"style":902},[901],[572,4677,4678,4681],{"style":905},[572,4679],{"className":4680,"style":910},[909],[572,4682,4684],{"className":4683},[622],[572,4685,4486],{"className":4686},[622],[572,4688,4689,4692],{"style":971},[572,4690],{"className":4691,"style":910},[909],[572,4693,4695],{"className":4694},[622],[572,4696,593],{"className":4697},[622],[572,4699,4700,4703],{"style":1023},[572,4701],{"className":4702,"style":910},[909],[572,4704,4706],{"className":4705},[622],[572,4707,697],{"className":4708},[622],[572,4710,959],{"className":4711},[958],[572,4713,4715],{"className":4714},[897],[572,4716,4718],{"className":4717,"style":1082},[901],[572,4719],{},[572,4721],{"className":4722,"style":884},[883],[572,4724],{"className":4725,"style":884},[883],[572,4727,4729],{"className":4728},[888],[572,4730,4732,4780],{"className":4731},[892,893],[572,4733,4735,4777],{"className":4734},[897],[572,4736,4738,4752,4763],{"className":4737,"style":902},[901],[572,4739,4740,4743],{"style":905},[572,4741],{"className":4742,"style":910},[909],[572,4744,4746,4749],{"className":4745},[622],[572,4747,1922],{"className":4748},[622],[572,4750,3232],{"className":4751},[622],[572,4753,4754,4757],{"style":971},[572,4755],{"className":4756,"style":910},[909],[572,4758,4760],{"className":4759},[622],[572,4761,4517],{"className":4762},[622],[572,4764,4765,4768],{"style":1023},[572,4766],{"className":4767,"style":910},[909],[572,4769,4771,4774],{"className":4770},[622],[572,4772,1922],{"className":4773},[622],[572,4775,3273],{"className":4776},[622],[572,4778,959],{"className":4779},[958],[572,4781,4783],{"className":4782},[897],[572,4784,4786],{"className":4785,"style":1082},[901],[572,4787],{},[572,4789,4791],{"className":4790},[2427],[572,4792,4794],{"className":4793},[2157,3406],[572,4795,4797,4817],{"className":4796},[892,893],[572,4798,4800,4814],{"className":4799},[897],[572,4801,4803],{"className":4802,"style":902},[901],[572,4804,4805,4808],{"style":3418},[572,4806],{"className":4807,"style":3422},[909],[572,4809,4810],{"style":3425},[3427,4811,4812],{"xmlns":3429,"width":3430,"height":3431,"viewBox":3432},[3434,4813],{"d":3660},[572,4815,959],{"className":4816},[958],[572,4818,4820],{"className":4819},[897],[572,4821,4823],{"className":4822,"style":1082},[901],[572,4824],{}," ist ",[572,4827,4829,4869],{"className":4828},[575],[572,4830,4832],{"className":4831},[579],[581,4833,4834],{"xmlns":583},[585,4835,4836,4866],{},[588,4837,4838,4840,4842,4844,4846,4848,4850,4852,4854,4856,4858,4860,4862,4864],{},[703,4839,1845],{},[595,4841,1848],{},[595,4843,1854],{},[591,4845,3219],{},[595,4847,3282],{},[591,4849,593],{},[595,4851,3282],{},[595,4853,1869],{"stretchy":698},[595,4855,1922],{},[591,4857,3273],{},[595,4859,1919],{"stretchy":698},[595,4861,1854],{},[595,4863,1922],{},[591,4865,3353],{},[601,4867,4868],{"encoding":603},"\\det = 2 \\cdot 3 \\cdot (-4) = -24",[572,4870,4872,4890,4908,4926,4953],{"className":4871,"ariaHidden":609},[608],[572,4873,4875,4878,4881,4884,4887],{"className":4874},[613],[572,4876],{"className":4877,"style":2062},[617],[572,4879,1845],{"className":4880},[2066],[572,4882],{"className":4883,"style":2077},[626],[572,4885,1854],{"className":4886},[2081],[572,4888],{"className":4889,"style":2077},[626],[572,4891,4893,4896,4899,4902,4905],{"className":4892},[613],[572,4894],{"className":4895,"style":641},[617],[572,4897,3219],{"className":4898},[622],[572,4900],{"className":4901,"style":627},[626],[572,4903,3282],{"className":4904},[631],[572,4906],{"className":4907,"style":627},[626],[572,4909,4911,4914,4917,4920,4923],{"className":4910},[613],[572,4912],{"className":4913,"style":641},[617],[572,4915,593],{"className":4916},[622],[572,4918],{"className":4919,"style":627},[626],[572,4921,3282],{"className":4922},[631],[572,4924],{"className":4925,"style":627},[626],[572,4927,4929,4932,4935,4938,4941,4944,4947,4950],{"className":4928},[613],[572,4930],{"className":4931,"style":4233},[617],[572,4933,1869],{"className":4934},[2151],[572,4936,1922],{"className":4937},[622],[572,4939,3273],{"className":4940},[622],[572,4942,1919],{"className":4943},[2427],[572,4945],{"className":4946,"style":2077},[626],[572,4948,1854],{"className":4949},[2081],[572,4951],{"className":4952,"style":2077},[626],[572,4954,4956,4959,4962],{"className":4955},[613],[572,4957],{"className":4958,"style":618},[617],[572,4960,1922],{"className":4961},[622],[572,4963,3353],{"className":4964},[622],[559,4966,4968],{"id":4967},"typische-fehler","Typische Fehler",[4970,4971,4972,5082,5085],"ul",{},[650,4973,4974,4975,5026,5027,5030,5031,5081],{},"Die Regel von Sarrus auf ",[572,4976,4978,4996],{"className":4977},[575],[572,4979,4981],{"className":4980},[579],[581,4982,4983],{"xmlns":583},[585,4984,4985,4993],{},[588,4986,4987,4989,4991],{},[591,4988,3273],{},[595,4990,597],{},[591,4992,3273],{},[601,4994,4995],{"encoding":603},"4 \\times 4",[572,4997,4999,5017],{"className":4998,"ariaHidden":609},[608],[572,5000,5002,5005,5008,5011,5014],{"className":5001},[613],[572,5003],{"className":5004,"style":618},[617],[572,5006,3273],{"className":5007},[622],[572,5009],{"className":5010,"style":627},[626],[572,5012,597],{"className":5013},[631],[572,5015],{"className":5016,"style":627},[626],[572,5018,5020,5023],{"className":5019},[613],[572,5021],{"className":5022,"style":641},[617],[572,5024,3273],{"className":5025},[622],"-Matrizen übertragen. Sie gilt ",[568,5028,5029],{},"nur"," für ",[572,5032,5034,5051],{"className":5033},[575],[572,5035,5037],{"className":5036},[579],[581,5038,5039],{"xmlns":583},[585,5040,5041,5049],{},[588,5042,5043,5045,5047],{},[591,5044,593],{},[595,5046,597],{},[591,5048,593],{},[601,5050,604],{"encoding":603},[572,5052,5054,5072],{"className":5053,"ariaHidden":609},[608],[572,5055,5057,5060,5063,5066,5069],{"className":5056},[613],[572,5058],{"className":5059,"style":618},[617],[572,5061,593],{"className":5062},[622],[572,5064],{"className":5065,"style":627},[626],[572,5067,597],{"className":5068},[631],[572,5070],{"className":5071,"style":627},[626],[572,5073,5075,5078],{"className":5074},[613],[572,5076],{"className":5077,"style":641},[617],[572,5079,593],{"className":5080},[622],"; für größere Matrizen nimmt man Laplace-Entwicklung oder Gauß-Elimination.",[650,5083,5084],{},"Die Nebendiagonalen addieren statt abziehen.",[650,5086,5087],{},"Bei der Laplace-Entwicklung das Vorzeichenschachbrett vergessen: Der mittlere Term der ersten Zeile hat ein Minus.",{"title":5089,"searchDepth":5090,"depth":5090,"links":5091},"",2,[5092,5093,5094],{"id":561,"depth":5090,"text":562},{"id":3183,"depth":5090,"text":3184},{"id":4967,"depth":5090,"text":4968},[5096,5099,5101,5103,5105,5107],{"lhs":5097,"rhs":5098},"a11*a22*a33 + a12*a23*a31 + a13*a21*a32 - a13*a22*a31 - a11*a23*a32 - a12*a21*a33","det([[a11, a12, a13], [a21, a22, a23], [a31, a32, a33]])",{"lhs":5100,"rhs":5098},"a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31)",{"lhs":5102,"rhs":3378},"2*3*4 + 0*2*1 + 1*1*1 - 1*3*1 - 2*2*1 - 0*1*4",{"lhs":5104,"rhs":3378},"det([[2, 0, 1], [1, 3, 2], [1, 1, 4]])",{"lhs":5106,"rhs":3378},"2*(3*4 - 2*1) - 0*(1*4 - 2*1) + 1*(1*1 - 3*1)",{"lhs":5108,"rhs":5109},"det([[2, 5, -1], [0, 3, 7], [0, 0, -4]])","2*3*(-4)","A = (a_{ij}) \\in \\mathbb{R}^{3 \\times 3}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmn>3\u003C\u002Fmn>\u003Cmo>×\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = (a_{ij}) \\in \\mathbb{R}^{3 \\times 3}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0361em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","determinant-3x3","\\det A = a_{11}a_{22}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32} - a_{13}a_{22}a_{31} - a_{11}a_{23}a_{32} - a_{12}a_{21}a_{33}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>11\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>22\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>33\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>12\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>23\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>31\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>13\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>21\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>32\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>13\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>22\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>31\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>11\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>23\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>32\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>12\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>21\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>33\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\det A = a_{11}a_{22}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32} - a_{13}a_{22}a_{31} - a_{11}a_{23}a_{32} - a_{12}a_{21}a_{33}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">11\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">22\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">33\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">12\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">23\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">31\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">13\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">21\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">32\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">13\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">22\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord 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reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">23\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord 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