If `A =[[1, -1] , [2, -1]]` , `B = [[x, 1], [y, -1]]` and `(A+B)^2 = A^2 + B^2` then `(x, y)` = 1) (1, 4) 2) (2,1) 3) (3,3) 4) (0,1)

If A=[[2 , 4 ,-1] , [-1 , 0 , 2]] , B=[[3 , 4], [-1 ,2] , [ 2 ,1]] , find (A B)^T .

If A= [[2,4,-1],[-1,0,2]], B=[[3,4],[-1,2],[2,1]] , Show that (AB)'=B'A' .

If A = [[-1, 2 ,3],[-1, 0, 2],[1, -3, 1]] and B = [[4,5,6],[-1, 0, 1], [2,1,2]], find 4A-3B

If A=[[2,3],[1,-4]] and B=[[1,-2],[-1,3]] , then verify that (A B)^(-1)=B^(-1)A^(-1)

Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such that A=B X , then X is equal to (a) 1/2[(2, 4), (3, -5)] (b) 1/2[(-2, 4), (3, 5)] (c) [(2, 4), (3,-5)] (d) none of these

If A=[[1 ,2,-3],[ 5, 0, 2],[ 1,-1, 1]], B=[[3,-1, 2],[ 4, 2 ,5],[ 2, 0, 3]] and C=[[4, 1, 2],[ 0, 3, 2],[ 1,-2, 3]] , then compute (A+B) and (B - C) . Also, verify that A + (B - C) = (A + B) - C .

If y^2=4b(x-c) and y^2 =8ax having common normal then (a,b,c) is (a) (1/2,2,0) (b) (1,1,3) (c) (1,1,1) (d) (1,3,2)

Determine the product [[-4, 4, 4], [-7, 1, 3],[5, -3, -1]][[1, -1, 1],[1, -2, -2],[2, 1, 3]] and use it to solve the system of equations x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1

Determine the product [[-4, 4, 4], [-7, 1, 3],[5, -3, -1]][[1, -1, 1],[1, -2, -2],[2, 1, 3]] and use it to solve the system of equations x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1

Compute the indicated products.(i) [[a, b],[-b ,a]][[a,-b],[b, a]] (ii) [[1],[ 2],[ 3]][[2, 3 ,4]] (iii) [[1,-2],[ 2 ,3]] [[1 ,2, 3],[ 2, 3 ,1]] (iv) [[2, 3 ,4 ],[3, 4 ,5],[ 4, 5, 6]][[1,-3, 5],[ 0, 2, 4],[ 3, 0, 5]] (v) [[2,1],[3,2],[-1,1]] [[1, 0, 1],[-1, 2 ,1]] (vi) [[3,-1, 3],[1,0,2]] [[2 ,-3],[ 1, 0],[ 3, 1]]