For which value of k, square matrix [ cc k & 8 4 & 2 k ] is non-i… - Vidyadip

Question

For which value of $k$, square matrix $\left[\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right]$ is non-invertible matrix?

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Answer

Suppose $A=\left|\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right|$
A is non-invertible, then $| A |=0$
$
\begin{aligned}
\Rightarrow & & \left|\begin{array}{cc}
k & 8 \\
4 & 2 k
\end{array}\right| & =0 \\
\Rightarrow & & 2 k^2-32 & =0 \\
\Rightarrow & & k^2 & =16 \\
\Rightarrow & & k & = \pm 4
\end{aligned}
$

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