The system of equations ( 1 - ) x + 3 y - 4 z = 0 x - ( 3 + ) y + 5 z = 0 3 x + y - z = 0 possesses non-trivial solutions for

Question

The system of equations

$(1 - λ) x + 3 y - 4 z = 0$

$x - (3 + λ) y + 5 z = 0$

$3 x + y - λ z = 0$

possesses non-trivial solutions for

Smart Achievers · Accepted Answer

(2)

$Put$ $| \begin{matrix} 1 - λ & 3 & - 4 \\ 1 & - (3 + λ) & 5 \\ 3 & 1 & - λ \end{matrix} |$ $= 0$

$\Rightarrow λ {(λ + 1)}^{2} = 0 \Rightarrow λ = - 1, 0$

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