सिद्ध कीजिए कि आव्यूह `A=[[1,-1,5],[-1,2,1],[5,1,3]]` एक सममित आव्यूह है।

If A=[[1, 1,-2],[ 2, 1,-3],[ 5, 4,-9]] . Find |A| .

Evaluate : [[1,3,5]][[1,0,3],[2,0,1],[0,1,2]][[1],[4],[6]]

The inverse of [(3,5,7),(2,-3,1),(1,1,2)] is :

(2) If A=[[2,3],[1,5]] then find A^(-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]]

Solve for X : [(1,2,-3),(2,1,3)]-X=[(5,1,8),(-6,0,5)] .

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]]

If A = |{:(1,1,-2),(2,1,-3),(5,4,-9):}| , find |A|.

If A=[(2 ,3,-5 ),(1, 2,-1)] and B=[(0, 5,1),(-2, 7, 3)] , find A+B and A-B

Find the rank of the matrix : [[-1,-3,3,-1],[1,1,-1,0],[2,-5,2,-3],[-1,1,0,1]]