`[[2,-3,1],[3,1,3],[-5,2,-4]]` `(A-lambda I)=0` characterstic equation`[[2-lambda,-3,1],[3,1-lamda,3],[-5,2,-4-lamda]]`

The matrix [(2,lambda,-4),(-1,3,4),(1,-2,-3)] is non singular , if :

If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so that A^2=5A+lambdaI

Compute the indicated products.(i) [[a, b],[-b ,a]][[a,-b],[b, a]] (ii) [[1],[ 2],[ 3]][[2, 3 ,4]] (iii) [[1,-2],[ 2 ,3]] [[1 ,2, 3],[ 2, 3 ,1]] (iv) [[2, 3 ,4 ],[3, 4 ,5],[ 4, 5, 6]][[1,-3, 5],[ 0, 2, 4],[ 3, 0, 5]] (v) [[2,1],[3,2],[-1,1]] [[1, 0, 1],[-1, 2 ,1]] (vi) [[3,-1, 3],[1,0,2]] [[2 ,-3],[ 1, 0],[ 3, 1]]

If the points A(-1,3,2),B(-4,2,-2)a n dC(5,5,lambda) are collinear, find the value of lambda .

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

If A=[[2/3, 1, 5/3],[ 1/3, 2/3, 4/3] ,[7/3, 2, 2/3]] and B=[[2/3, 3/5, 1],[ 1/5, 2/5, 4/5],[ 7/3, 6/5, 2/5]] , then compute 3A - 5B .

If A=[[2,3,4],[-3,0,2]], B=[[3,-4,-5],[1,2,1]] and C=[[5,-1,2],[7,0,3]] , find the matrix X such that 2A+3B=X+C

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

"Let "plambda^(4) + qlambda^(3) +rlambda^(2) + slambda +t =|{:(lambda^(2)+3lambda,lambda-1, lambda+3),(lambda+1, -2lambda, lambda-4),(lambda-3, lambda+4, 3lambda):}| be an identity in lambda , where p,q,r,s and t are constants. Then, the value of t is..... .