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Given 2 x-y+2 z=1 , x-2 y+z=-4 , and x+y...

Given `2 x-y+2 z=1 , x-2 y+z=-4 ,` and `x+y+lambda z =4`. Then the. value of `lambda` such that the given system of equation has no solution is

A

3

B

1

C

0

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, given system has no solution.
`therefore Delta = 0` and any one amongst `Delta_(x), Delta_(y), Delta_(z)` is non-zero.
Let `|{:(2, -1, 2), (1, -2, 1), (1, 1, lambda) = 0 " and " Delta_(z) = |{:(2, -1, 2), (1, -2, -4), (1, 1, 4) = 6 ne 0`
`rArr lambda = 1`
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