Let M be a `3xx3` matrix satisfying `M[[0],[1],[0]]=[[-1],[2],[3]],`
`M[[1],[-1],[1]]=[[1],[1],[-1]] and M [[1],[1],[1]]=[[0],[0],[12]]`

Let M be a 3xx3 matrix satisfying M[[0], [1] ,[0]]=[[-1], [2], [3]] , M[[1],[-1], [0]]=[[1], [1],[-1]] ,and M[[1], [1], [1]]=[[0] ,[0], [12]] Then the sum of the diagonal entries of M is _________.

Let M be a 3xx3 matrix satisfying M[0 1 0]=[-1 2 3] ,M[1-1 0]=[1 1-1],a n dM[1 1 1]=[0 0 12] Then the sum of the diagonal entries of M is _________.

Let A is 3 xx 3 matrix such that Ax_1=B_1,Ax_2=B_2,Ax_3=B_3 where x_1=[[1],[1],[1]],x_2=[[0],[2],[1]],x_3=[[0],[0],[1]] ,br> B_1=[[1],[0],[0]],B_2=[[0],[2],[0]],B_3=[[0],[0],[2]] then find |A| .

Find the matrix X satisfying the equation: [[2, 1 ],[5, 3]]X[[5, 3],[ 3 ,2]]=[[1, 0],[ 0 ,1]] .

Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1 1]=[0 0 12] Then the sum of the diagonal entries of M is _________.

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three column matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The value of det(B^(-1)) , is

Find the rank of matrix.A= [[3,1,2,0],[1,0,-1,0],[2,1,3,0]]

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisgying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). find sin^(-1) (detA) + tan^(-1) (9det C)

Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)] , then find A^(-1) .