Solve `|[-lambda^(2),1,1],[1,-lambda^(2),1],[1,1,-lambda^(2)]|=0`

[" 2.Let matrix "A=[[1,y,4],[2,2,z]]" ; if "xyz=2 lambda" and "8x+4y+3z=lambda+28," then "(adj A)" A equals: "],[[" (A) "[[lambda+1,0,0],[0,lambda+1,0],[0,0,lambda+1]]," (B) "[[lambda,0,0],[0,lambda,0],[0,0,lambda]]],[" (C) "[[lambda^(2),0,0],[0,lambda^(2),0],[0,0,lambda^(2)]]," (D) "[[lambda+2,0,0],[0,lambda+2,0],[0,0,lambda+2]]]]

Find the values of lambda for which 3-lambda,-1,1-1,5-lambda,-11,-1,3-lambda]|=0

For a non zero " lambda" ,the value of matrix "[[lambda,1,0],[0,lambda,1],[0,0,lambda]]^(n) " is equal to

If a lambda^(4)+b lambda^(3)+c lambda^(2)+d lambda+e = |[lambda^(2)-3,-1,lambda+sqrt(3)],[lambda^(2)+lambda,2 lambda-4,3 lambda+1],[lambda^(2)-3 lambda,3 lambda+5,lambda-3]| then |a| equals

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C , where A, B and C are matrices then find matrices B and C.

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C, where A, B and C are matrices then A+B=

If a lambda^(4)+b lambda^(3)+c lambda^(2)+d lambda+e=|[lambda^(2)-3,lambda-1,lambda+sqrt(3)],[lambda^(2)+lambda,2 lambda-4,3 lambda+1],[lambda^(2)-3 lambda,3 lambda+5,lambda-3]| then |a| equals

A=[[2-lambda,-1,0-1,2-lambda,-10,-1,2-lambda]] then find out

If |[lambda^(2),-lambda,2 lambda-1],[lambda+2,1-lambda,lambda],[lambda+2,lambda+1,-lambda]|=a lambda^(4)+b lambda^(3)+c lambda^(2)+d lambda+e Then values of a, b, c, d and e are.

Show that if lambda_(1), lambda_(2), ...., lamnda_(n) are n eigenvalues of a square matrix a of order n, then the eigenvalues of the matric A^(2) are lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2) .