The system of equations 2x+y−z=7; x−3y+2z=1, x+4y+λz=k where λ,k∈R has infinitely many solutions then −λ+k=............

Δ=|21−11−3214λ|=0 λ=−3Δ1=|7−1−11−32k+4−3|=0⇒k=6 K−λ=6+3=9

The system of equations 2x+y−z=7; x−3y+2z=1, x+4y+λz=k where λ,k∈R has infinitely many solutions then −λ+k=............

Δ=|21−11−3214λ|=0 λ=−3Δ1=|7−1−11−32k+4−3|=0⇒k=6 K−λ=6+3=9

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The system of equations $2 x + y - z = 7; x - 3 y + 2 z = 1, x + 4 y + λ z = k$ where $λ, k \in R$ has infinitely many solutions then $- λ + k = ............$

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Detailed Solution

$Δ = | \begin{matrix} 2 & 1 & - 1 \\ 1 & - 3 & 2 \\ 1 & 4 & λ \end{matrix} | = 0 λ = - 3$

$Δ_{1} = | \begin{matrix} 7 & - 1 & - 1 \\ 1 & - 3 & 2 \\ k & + 4 & - 3 \end{matrix} | = 0 \Rightarrow k = 6 K - λ = 6 + 3 = 9$

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