Compute the determinant of the following 6x6 matrix using patterns, being careful to show your steps:...

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Compute the determinant of the following 6x6 matrix using patterns, being careful to show your steps: 000002) -100000 0 50000 0 1 0 0 0 0 0 00300 00010/ 0 (b) (3 points) Compute the determinant of the following 5x5 matrix using patterns, being careful to show your steps: (10 3 0 0 20100 00010 01002 0 2001/ (c) (5 points) Find the determinant of the 100x100 matrix corresponding to a linear trans- formation T that acts the standard basis vectors ₁.2...100 in the following fashion. T(ei) = €₂, T(₂) = €3₁ : T(€99) = €100, T(€100) = ei. That is, T takes each of the first 99 standard basis vectors to the subsequent standard basis vector, and T takes the last standard basis vector to the first standard basis vector. Be sure to justify all your reasoning. Compute the determinant of the following 6x6 matrix using patterns, being careful to show your steps: 000002) -100000 0 50000 0 1 0 0 0 0 0 00300 00010/ 0 (b) (3 points) Compute the determinant of the following 5x5 matrix using patterns, being careful to show your steps: (10 3 0 0 20100 00010 01002 0 2001/ (c) (5 points) Find the determinant of the 100x100 matrix corresponding to a linear trans- formation T that acts the standard basis vectors ₁.2...100 in the following fashion. T(ei) = €₂, T(₂) = €3₁ : T(€99) = €100, T(€100) = ei. That is, T takes each of the first 99 standard basis vectors to the subsequent standard basis vector, and T takes the last standard basis vector to the first standard basis vector. Be sure to justify all your reasoning.

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