Determine the value of $k$ for which the system \begin{cases} x + y + 2z = 1 \ x + 2y - 3z = -3 \ 7x + 15y + kz = -24 \end{cases} has no solutions.
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Step 1: Write the system of equations in matrix form: \[ \begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & -3 \\ 7 & 15 & k \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ -3 \\ -24 \end{bmatrix} \] Show more…
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