Bautista 02 test

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1 0 0 0 1 1 0 1 1 1 (a) Find the matrix representing L with respect to S and T. (b) Find a basis for the kernel of L. (c) Find a basis for the range space of L. 6. Find the determinant of the matrix A: [20] "2 10 0" 12 10 0 12 1 0 0 1 2 7. Determine if the matrix below is diagonalizable or not. If it is diagonalizable, find a diagonalizing matrix: [30] "5 -2 - 2 " 0 1 0 4 -2 -1

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Bautista 02 test

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1 0 0 0 1 1 0 1 1 1

(a) F i n d the matr ix representing L w i th respect to S and T.

(b) F i n d a basis for the kernel of L .

(c) F i n d a basis for the range space of L .

6. F i n d the determinant of the matr ix A : [20]

"2 1 0 0" 1 2 1 0 0 1 2 1 0 0 1 2

7. Determine if the matr ix below is diagonalizable or not. If it is diagonalizable, find a diagonalizing matrix: [30]

" 5 - 2 - 2 " 0 1 0 4 - 2 - 1