Let `p=[(3,-1,-2),(2,0,alpha),(3,-5,0)],` where `alpha in RR.` Suppose `Q=[q_(ij)]` is a matrix such that `PQ=kl,` where `k in RR, k != 0 and l` is the identity matrix of order 3. If `q_23=-k/8 and det(Q)=k^2/2,` then

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kI, where k in RR, k != 0 and I is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kI, where k in RR, k != 0 and I is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kI, where k in RR, k != 0 and I is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

Let P=[(3,-1,-2),(2,0,alpha),(3,-5,0)] , where alpha in R . Suppose Q =[q_(ij)] is a matrix satisfying PQ = KI_3 for some non - zero K in R . If q_(23) =- (K)/(8) and |Q| = (1)/(2), then alpha^2 + k^2 is equal to ________.

If A=[(1,0),(-1,7)] and l is an identity matrix of order 2, then the value of k, if A^(2)=8A+kI , is :

Let P = {:[(1,0,0),(4,1,0),(16,4,1)] and I be te identity matrix of order 3. If Q = [q_(ij)] is A matrix such that P(50)-Q=I is then q31+q32/q21. The value of

If A=[(k,2,3),(-2,0,5),(-3,-5,0)] is a skew symmetric matrix then k =

Let P=[[1,0,04,1,016,4,1]] and I be the identity matrix of order 3. If Q=[qij] is a matrix, such that P^(50)-Q=I, then (q_(31)+q_(32))/(q_(21)) equals

If A=[(2,3),(1,0)]=P+Q , where P is symmetric and Q is skew-symmetric, then find the matrix P.

Let P=[[1,0,0],[4,1,0],[16,4,1]] and I be the identity matrix of order 3 . If Q = [q_()ij ] is a matrix, such that P^(50)-Q=I , then (q_(31)+q_(32))/q_(21) equals