Find the value of $k$ for which the system of equations $k x + y = 2, x + k y = 1$ is undefined.

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Solution

The system of equation $k x + y = 2, x + k y = 1$ will be undefined if
$\frac{k}{1} = \frac{1}{k} \neq \frac{2}{1}$
or, $\frac{k}{1} = \frac{1}{k}$
or, $k^{2} = 1$
or, $k = \pm 1$ .
So for $k = \pm 1$ the given system of equations will be undefined.

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