" iv ")hwA=[[1,5],[-1,2]]

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:(i) [[3, 5],[ 1,-1]] (ii) [[6,-2, 2],[-2, 3,-1],[ 2,-1, 3]] (iii) [[3, 3,-1],[-2,-2, 1],[ 4, 5, 2]] (iv) [[1 ,5],[-1, 2]]

Select the correct option from the given alternatives. If A = [[1,2],[3,-5]] , then adj A is i] [[-5,-2],[-3,1]] ii] [[3,-5],[1,2]] iii] [[2,3],[-5,1]] iv] [[-5,3],[2,1]]

Select and write the most appropriate answer from the given alternative of the following If A = [[1,2],[3,-5]] then adjA is i] [[-5,-2],[-3,1]] ii] [[3,-5],[1,2]] iii] [[2,3],[-5,1]] iv] [[-5,3],[2,1]]

Express the following matrices as the sum of a symmetric and a skew symmetric matrix : (i) [{:(3,5),(1,-1):}] (ii) [{:(6,-2,2),(-2,3,-1),(2,-1,3):}] (iii) [{:(3,3,-1),(-2,-2,1),(-4,-5,2):}] (iv) [{:(1,5),(-1,2):}]

Select and write the most appropriate answer from the given alternative of the following If A = [[2,3],[5,-2]] , then A^-1= i] A^2 ii] frac{1}{19}A iii] frac{1}{17}A iv] frac{1}{15}A

If A = [(2,2,1), (1,3,1), (1,2,2)] then A^-1+(A-5I) (AI)^2 = (i) 1/ 5 [[4,2, -1], [-1,3,1], [-1,2,4]] (ii) 1/5 [[4, -2, -1], [-1, 3, -1], [-1, -2,4]] (iii) 1/3 [[4,2, -1], [-1,3,1], [-1,2,4]] (iv) 1/3 [[4, -2, -1], [-1,3, -1], [-1, -2,4]]

" (i) |[2,5], [6,0]| (ii) |[2,-1],[3,2]| (iii) |[0,4],[5,-1]| (iv) |[(1)/(2),1],[(3)/(4),(1)/(5)]|

Compute the adjoint of each of the following matrices: [[1, 2, 2],[ 2 ,1 ,2],[ 2, 2, 1]] (ii) [[1, 2, 5],[ 2, 3,1],[-1, 1, 1]] (iii) [[2,-1, 3],[ 4, 2, 5],[ 0, 4,-1]] (iv) [[2, 0,-1],[ 5, 1, 0],[ 1, 1, 3]] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.