If `plambda^4+qlambda^3+rlambda^2+slambda+t=|lambda^2+3lambdalambda-1lambda+3lambda^2+1 2-lambdalambda-3lambda^2-3lambda+4 3lambda|` , then `p=` `-5` (2) `-4` (3) `-3` `-2`

If plambda^4+qlambda^3+rlambda^2+slambda+t=|(lambda^2+3lambda,lambda-1,lambda+3),(lambda+1,2-lambda,lambda-4),(lambda-3,lambda+4,3lambda)|, then value of t is

"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..... .

p(lambda)^4+q(lambda)^3+r(lambda)^2+s(lambda)+t = |((lambda^2 + 3lambda) , lambda -1 , lambda+3) , (lambda +1 , -2lambda , lambda-4 ) ,(lambda-3 , lambda+4 , 3lambda)| find t=?

Let p lambda^(4)+q lambda^(3)+r lambda^(2)+s lambda+t=|[lambda^(2)+3 lambda,lambda-1,lambda-3],[lambda-1,-2 lambda,lambda-4],[lambda-3,lambda+3,3 lambda]| be an identity in lambda ,where p,q,r,s and t are constants.Then the value of t is

If |[lambda^(2)+3 lambda,lambda-1,lambda+3],[lambda+1,2-lambda,lambda-4],[lambda-3,lambda+4,3 lambda]|=p lambda^(4)+q lambda^(3)+r lambda^(2)+s lambda+t then t=

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 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

lambda ^ (3) -6 lambda ^ (2) -15 lambda-8 = 0

If the matrix A = [[lambda_(1)^(2), lambda_(1)lambda_(2), lambda_(1) lambda_(3)],[lambda_(2)lambda_(1),lambda_(2)^(2),lambda_(2)lambda_(3)],[lambda_(3)lambda_(1),lambda_(3)lambda_(2),lambda_(3)^(2)]] is idempotent, the value of lambda_(1)^(2) + lambda_(2)^(2) + lambda _(3)^(2) is

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.