Find the matrix `A` such that : `[(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)]` (ii) `A[(1, 2, 3 ),(4, 5 ,6)]=[(-7,-8,-9 ),(2, 4 ,6)]`

Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}]

Find the rank of matrix A = [(4,5,-6,1),(7,-3,0,8)] .

Find the matrix X so that X[[1 ,2 ,3], [4, 5 ,6]]=[[-7,-8,-9],[2,4,6]]

Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]] = [[-7,-8,-9],[2,4,6]]

Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]] = [[-7,-8,-9],[2,4,6]]

Find the matrix X for which: [(3, 2), (7, 5)]X[(-1, 1),(-2, 1)]=[(2,-1),( 0, 4)] .

If A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is (a) [(2, 2,-4 ),(2, 3, 4),(-4, 4, 2)] (b) [(2, 4,-5),( 0, 3, 7),(-3, 1, 2)] (c) [(4, 4,-8),( 4, 6, 8),(-8, 8, 4)] (d) [(1, 0 ,0 ),(0 ,1 ,0),( 0, 0, 1)]

Find the matrix A such that : [4 1 3]A=[-4 8 4-1 2 1-3 6 3] (iv) [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

Find a matrix A such that 2A-3B+5C=O , where B=[[-2, 2, 0],[ 3, 1 ,4]] and C=[[2, 0,-2], [7, 1, 6]] .