Q.

The values of λfor which the system of equationsλ+5x+λ−4y+z=0, λ−2x+λ+3y+z=0, λx+λy+z=0 has a non-trivial solution is

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a

-1,2

b

0,-1

c

0

d

Non of these

answer is D.

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Detailed Solution

Δ=λ+5λ-41λ-2λ+31λλ1R1→R1-R2,R2→R2-R3=7-70-230λλ1=7(3-0)+7(-2-0)+0(-2λ-3λ)=21-14=7≠0∴The given system has only zero solution.
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The values of λfor which the system of equationsλ+5x+λ−4y+z=0, λ−2x+λ+3y+z=0, λx+λy+z=0 has a non-trivial solution is