The value of $k \in R,$ for which the following system of linear equations
$3 x - y + 4 z = 3,$
$x + 2 y - 3 z = - 2,$
$6 x + 5 y + k z = - 3,$
has infinitely many solutions, is:

- 3

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Solution

The correct option is B $- 5$
$\Rightarrow Δ = ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & 4 1 & 2 & - 3 6 & 5 & k \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow k = - 5$
For, $k = - 5, Δ_{1} = Δ_{2} = Δ_{3} = 0$

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The value of k∈R, for which the following system of linear equations 3x–y+4z=3, x+2y–3z=–2, 6x+5y+kz=–3, has infinitely many solutions, is:

The correct option is B −5⇒Δ=∣∣ ∣∣3−1412−365k∣∣ ∣∣=0⇒k=−5 For, k=−5,Δ1=Δ2=Δ3=0

The value of $k \in R,$ for which the following system of linear equations
$3 x - y + 4 z = 3,$
$x + 2 y - 3 z = - 2,$
$6 x + 5 y + k z = - 3,$
has infinitely many solutions, is:

The correct option is B $- 5$
$\Rightarrow Δ = ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & 4 1 & 2 & - 3 6 & 5 & k \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow k = - 5$
For, $k = - 5, Δ_{1} = Δ_{2} = Δ_{3} = 0$