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QUESTION

For what values of $\alpha$ does the set of equations
\begin{eqnarray*}
\alpha x+y&=&0\\4x+\alpha y&=&0
\end{eqnarray*}
have a non-trivial (non-zero) solution? (Do NOT solve the
equations).

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ANSWER

The equations
\begin{eqnarray*}
\alpha x+y&=&0\\4x+\alpha y&=&0
\end{eqnarray*}
have a non-trivial solution if
$\left|\begin{array}{cc}\alpha&1\\4&\alpha
\end{array}\right|=\alpha^2-4=0,\ \alpha=\pm2$




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