Matrices · Question 16

Let S = \m Z : Am2 + Am = 3I - A-6 \, where A = bmatrix 2 & -1 \ 1 & 0 bmatrix. Then n(S) is equal to .

Let M denote the set of all real matrices of order 3 3 and let S = \-3, -2, -1, 1, 2\. Let S1 = \A = [aij] M : A = AT and aij S, i, j\, S2 = \A = [aij] M : A = -AT and aij S, i, j\, S3 = \A = [aij] M : a11 + a22 + a33 = 0 and aij S, i, j\. If n(S1 S2 S3) = 125 , then equals .

Let A = bmatrix 1 2 & -2 \ 0 & 1 bmatrix and P = bmatrix & - \ & bmatrix, > 0. If B = PAP , C = P B10P and the sum of the diagonal elements of C is mn, where (m, n) = 1, then m + n is :

1. 127
2. 2049
3. 258
4. 65