System of linear equations

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If the system of equations $3 x - 2 y + z = 0, λ x - 14 y + 15 z = 0, x + 2 y + 3 z = 0$ has a non-trivial solution then $λ$ =

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Solution

$G i v e n s y s t e m o f e q u a t i o n s h a s n o n - t r i v i a l s o l u t i o n \Rightarrow Δ = 0$
$\begin{array}{l} \Rightarrow |\begin{matrix} 3 & - 2 & 1 \\ λ & - 14 & 15 \\ 1 & 2 & 3 \end{matrix}| = 0 \\ \Rightarrow 3 (- 42 - 30) + 2 (3 λ - 15) + 1 (2 λ + 14) = 0 \\ \Rightarrow - 216 + 6 λ - 30 + 2 λ + 14 = 0 \\ \Rightarrow 8 λ = 232 \\ \Rightarrow λ = 29 \end{array}$

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System of linear equations

Remember concepts with our Masterclasses.

If the system of equations 3x−2y+z=0, λx−14y+15z=0, x+2y+3z=0 has a non-trivial solution then λ=

Given system of equations has non-trivial solution⇒Δ=0⇒3-21λ-1415123=0⇒3-42-30+23λ-15+12λ+14=0⇒-216+6λ-30+2λ+14=0⇒8λ=232⇒λ=29

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If the system of equations $3 x - 2 y + z = 0, λ x - 14 y + 15 z = 0, x + 2 y + 3 z = 0$ has a non-trivial solution then $λ$ =