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

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

Find all values of lambda for which the (lambda-1)x+(3 lambda+1)y+2 lambda z=0(lambda-1)x+(4 lambda-2)y+(lambda+3)z=02x+(3 lambda+1)y+3(lambda-1)z possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0, (lambda-1)x+(4lambda-2)y+(lambda+3)z=0, 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

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

Number of real values of lambda for which the matrix A=[[2,-1,32,-1,3lambda+3,lambda-2,lambda+7]] has no inverse (A) 0(B)1(C)2(D) infinite ]]