Comprehension 2 Consider the system of linear equations `alphax+y+z=m x+alphay+z=n x+y+alphaz=p` If `alpha=1\ &\ m!=p` then the system of linear equations has- a. no solution b. `\ ` infinite solutions c. unique solution d. `\ ` unique solution `if\ p=n`

Options

A. The given system of equation has no solution if `alpha=-2` and `m+n+pne0`
B. The give system of equation has no solution if `alpha=1` and `m ne n` or `n ne p` or `p ne m`
C. The given system of equation has infinite solution if `alpha=-2` and `m+n+p=0`
D. The given system of equation has unique solution if `alpha=1` or `-2`

Answer

A, B, C

Explanation

`D|{:(alpha,1,1),(1,alpha,1),(1,1,alpha):}|=(alpha-1)^(2)(alpha+2)`
`D_(1)=|{:(m,1,1),(n,alpha,1),(p,1,alpha):}|=(alpha-1)[m(alpha+1)-(n+p)]`
`D_(2)=(alpha-1)[n(alpha+1)-(m+p)]`
`D_(3)=(alpha-1)[p(alpha+1)-(m+n)]`