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 .2...100 in the following fashion. T(ei) = , T() = 3 : 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.