Consider the system $x + y + kz = 0$ $2x + ky + 4z = 0$ $kx + 2y + 4z = 0$ where $k$ is some constant. For what value(s) of $k$ does this system have an infinite one-parameter family of solutions? An infinite two-parameter family of solutions? A unique solution?
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Step 1: The augmented matrix of the system is: $\begin{bmatrix} 1 & 1 & k & 0 \\ 2 & k & 4 & 0 \\ k & 2 & 4 & 0 \end{bmatrix}$ Show more…
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