" 14.Prove that "|[x+lambda,x,x],[x,x+lambda,x],[x,x,x+lambda]|=lambda^(2)(3x+lambda)

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

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

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

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):}|

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 prove that A^(-1) exists if 3x+lambda ne0, lambda=ne0

Let f be a real valued function such that for any real x, f(lambda+x)=f(lambda-x) and f(2lambda+x)=f(2lambda-x) for some lambda>0 . Then

A system of equations lambda x+y+z=1,x+lambda y+z=lambda,x+y+lambda z=lambda^(2) have no solution then value of lambda is

the values of lambda for which (lambda^(2)-3 lambda+2)x^(2)+(lambda^(2)-5 lambda+6)+lambda^(2)-4=0 is identity in x is