If matrix `A=[1-1-1 1]` and `A^2=k A ,` then write the value of `kdot`

If the matrix A=[(1,-1),(-1,1)] and A^(2)=kA ,then write the value of k

Let the matrix A and B defined as A=|[3,2] , [2,1]| and B=|[3,1] , [7,3]| Then the value of |det(2A^9 B^(-1))|=

Let S_k,k=1, 2, …. 100 denote the sum of the infinite geometric series whose first term is (k-1)/(K!) and the common ration is 1/k then the value of (100)^2/(100!)+underset(k=1)overset(100)Sigma|(k^2-3k+1)S_k| is ____________

If x = 1 is a zeru of the polynomial f(x) = x^(3) - 2x^(2) + 4x + k , write the value of k.

A variable plane at a distance of 1 unit from the origin cuts the coordinate axes at A,B and C satisfies the relation 1/x^2+1/y^2+1/z^2= k , then the value of k is :

A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1-k)/(6), (1+2k)/(6), (1-k)/(6), (1+k)/(6), (1-2k)/(6) and (1+k)/(6) , respectively. If two such thrown and the probability of getting a sum equal to lies between (1)/(9) and (2)/(9) , then the integral value of k is

If the adjoint of a 3xx3 matrix P is [(1,4,4),(2,1,7),(1,1,3)] then the possible value (s ) of the determinant of P 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 value of det(B^(-1)) , 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