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Question: If \(x + y - z = 0,3x - \alpha y - 3z = 0,x - 3y + z = 0\) has non zero solution, then \(\alpha =\)...

If x+y−z=0,3x−αy−3z=0,x−3y+z=0x + y - z = 0,3x - \alpha y - 3z = 0,x - 3y + z = 0 has non zero solution, then α=\alpha =

A

– 1

B

0

C

1

D

– 3

Answer

– 3

Explanation

Solution

The given system of homogeneous equations has a non-zero solution if, Δ=0\Delta = 0

i.e., ∣11−13−α−31−31∣=−2α−6=0\left| \begin{matrix} 1 & 1 & - 1 \\ 3 & - \alpha & - 3 \\ 1 & - 3 & 1 \end{matrix} \right| = - 2\alpha - 6 = 0,i.e. if α=−3\alpha = - 3.