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If `A=[[1,2,2],[2,1,-2],[a,2,b]]` is a matrix satisfying the equation `text(A)A^T =9I`, where `I` is 3x3 identity matrix, then the ordered pair (a,b) is equal to
Let X and Y be two arbitrary, 3 x3, non zero, skew-symmetric matrices and Z be an arbitrary 3x3, ilon zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
If `A=[[alpha,2],[2,alpha]]` and `|A^3|=125` then the value of `alpha` is
`A=[[1,0,0],[0,1,1],[0,-2,4]]` and `I=[[1,0,0],[0,1,0],[0,0,1]]` and `A^(-1)=[1/6(A^2+cA+dI)],`then the value of c and d are
Let `P =[a_(ij)]` be a 3 x 3 matrix and let `Q=[b_(ij)]`, where `b_(ij)=2^(i+j)a_(ij)` for `1<=i,j<=3`. lf the determinant of P is 2, then the determinant of the matrix Q is
Let `A=([1,-1,1],[2,1,-3],[1,1,1])` and `10B=([4,2,2],[-5,0,alpha],[1,-2,3])` If B is the inverse of matrix A, then `alpha` is
The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0, is
Let P and Q be 3 x 3 matrices `P !=Q`. If `P^3=Q^3` and `P^2Q=Q^2P` then determinant of `(P^2+ Q^2)` is equal to:
If `P= [[1,alpha,3],[1,3,3],[2,4,4]]` is the adjoint of a `3xx3` matrix A and |A|=4, then `alpha` is equal to:
If matrix `A=[[a,b,c],[b,c,a],[c,a,b]]`[where a, b, c are real positive numbers, abc=1 and `A^TA=I`, then the value of `a^3 + b^3 + c^3=`
The number of 3 x 3 matrices A whose entries are either 0 or 1 and for which the system `A[[x],[y],[z]]=[[1],[0],[0]]` has exactly two distinct solution, is
If P is a 3 x3 matrix such that `P^T=2P+I`, where `P^T` is the transpose of P and I is the 3 x 3 identity matrix, then there exists a column matrix `X= [[x],[y],[z]] !=[[0],[0],[0]]` such that
If `A= [[3,2],[0,1]]`, then `(A^-1)^3` is equal to
`|[a+b,a+2b,a+3b],[a+2b,a+3b,a+4b],[a+4b,a+5b,a+6b]|`=
`|[b^2+c^2,a^2,a^2],[b^2,c^2+a^2,b^2],[c^2,c^2,a^2+b^2]|`=
If `2A+3B=[[2,-1,4],[3,2,5]]` and `A+2B= [[5,1,3],[1,6,2]]`, then B=
If `Delta_1=|[x,b,b],[a,x,b],[a,a,x]|` and `Delta_2= |[x,b],[a,x]|` then
If `Delta(x)=|[1,x,x+1],[(2x),x(x-1),x(x+1)],[3x(x-1),x(x-1)(x-2),x(x^2-1)]|` then `Delta(100)` equals
If y=cos(mx), then the determinant `Delta =|[y,y_1,y_2],[y_3,y_4,y_5],[y_6,y_7,y_8]|` where `y_r=(d^ry)/(dx^r)`, equals
The determinant `Delta =|[a,a+b,a+2b],[a+2b,a,a+b],[a+b,a+2b,a]|` equals
