The number of values of k for which the linear equations `4x""+""k y""+""2z""=""0` `k x""+""4y""+""z""=""0` `2x""+""2y""+""z""=""0` posses a non-zero solution is : (1) 3 (2) 2 (3) 1 (4) zero

Options

A. zero
B. 3
C. 2
D. 1

Answer

3

Explanation

For non-trivial solution of the given system of linear equations
`|{:(4,,k,,2),(k,,4,,1),(2,,2,,1):}|=0`
`rArr 8+ k (2-k) + 2 (2k -8) =0`
`rArr -k^(2) +6k -8 =0`
`rArr k^(2) -6k +8=0`
`rArr k=2,4`
Clearly there exists two values of k .