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The system of linear equations x+y-z=6, ...

The system of linear equations `x+y-z=6, x+2y-3z=14` and `2x+5y-lambda z=9` has a unique solution (A) `lambda=8` (B) `lambda !=8` (C) `lambda=7` (D) `lambda !=7`

Text Solution

Verified by Experts

For a system of linear equations having unique solution, value of the determinant should not be `0`.
Here, `Delta = |[1,1,-1],[1,2,-3],[2,5,-lambda]| != 0`
`=>[-2lambda+15-1(-lambda+6)-(5-4)] != 0`
`=>-lambda+8 != 0`
`=>lambda !=8`
So, option `B` is the correct option.
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