Let A be a 3 3 matrix such that A + A ^ T = O . If A [ array c 1 \\ -1 \\ 0 array ]= [ array l 3 \\ 3 \\ 2 array ], A ^ 2 [ array c 1 \\ -1 \\ 0 array ]= [ array c -3 \\ 19 \\ -24 array ] and det ( adj (2 adj ( ~A + I )))=(2)^ (3)^ (11)^ , , , are non-negative integers, then + + is equal to \_\_\_\_
A. A
A is skew-symmetric: A = bmatrix 0 & -c & b\ & 0 & -a\\-b & a & 0 bmatrix . From A bmatrix 1\\-1\\0 bmatrix = bmatrix 3\\3\\2 bmatrix : c = 3, a+b = -2. From A^2 bmatrix 1\\-1\\0 bmatrix = bmatrix -3\\19\\-24 bmatrix : b = 3, a = -5. A+I = bmatrix 1&-3&3\\3&1&5\\-3&-5&1 bmatrix , (A+I) = 44. For 3 3 matrix: ( adj (M)) = ( M)^2. (2\, adj (A+I)) = 8 44^2 = 8 1936 = 15488 = 2^7 11^2. ( adj (2\, adj (A+I))) = 15488^2 = 2^ 14 11^4. = 14,\ = 0,\ = 4. + + = 18.
Related: Mathematics — Matrices · All PYQ Banks