Let `alpha,lambda,mu in R,` Consider the system of linear equations `alphax+2y=lambda, 3x-2y=mu` Which of the following statement (s) is (are) correct?

Options

A. If `alpha =-3` then the system has infinitely many solutions for all values of `lambda " and "mu`
B. If `alpha ne -3` then the system has a unique solution for all values of `lambda " and " mu`
C. If `lambda +mu =0` then the system has infiniely many solutions for `alpha =-3`
D. if `lambda +mu ne 0` then the system has no solution for `alpha =-3`

Answer

2,3,4

Explanation

`alphax +2y=lambda`
`3x-2y=mu`
`Delta = |{:(alpha,,2),(3,,-2):}|=-2alpha-6`
`Delta =0, :. , alpha =-3`
`Delta_(1) = |{:(lambda,,2),(mu,,-2):}|=-2lambda -2mu =-2(lambda +mu)`
`Delta_(2)= |{:(-3,,lambda),(3,,mu):}|=-3mu -3lambda =-3(lambda-mu)`
Now check options