Let `A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]`then prove that `A^(-1)` exists if `3x+lambda ne0, lambda=ne0`

Let A=[(x+lambda,x,x), (x,x+lambda,x), (x,x,x+lambda)]. Then A^(-1) exists if (A) xne0 (B) lambdane0 (C) 3x+lambdane0, lambdane0 (D) xne0,lambdane0

Let A=[[x+lambda,x,x] , [x,x+lambda,x] ,[x,x,x+lambda]] then A^(-1) exists if (A) x!=0 (B) lambda!=0 (C) 3x+1!=0 , lambda!=0 (D) x!=0 , lambda!=0

Evaluate the following : |{:(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lambda):}|

If |(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lambda)| = 0, (lambda != 0) then a) x = - lambda//3 b) x = 3 lambda c)x = 0 d)None of these

If f(x)=|[x+lambda,x,x] , [x,x+lambda,x] , [x,x,x+lambda]| then f(12x)-f(x)=

Let f(x) = [{:(5^(1//x),x lt 0),(lambda[x],x le 0","lambda in R):} , then at x = 0 :

lim_(x rarr oo)((x+lambda)/(x-lambda))^(x)=4 then lambda

|[x+lambda, 2x, 2x], [2x, x+lambda, 2x], [2x, 2x, x+lambda]| =(5x+ lambda)(lambda-x)^(2)

The roots of det[[x,a,b,1lambda,x,b,1lambda,mu,x,1lambda,mu,v,1]]=0 are