Find k, if the following matrices are singular : [ ccc K-1 & 2 & … - Vidyadip

Question

Find k, if the following matrices are singular : $\left[\begin{array}{ccc}K-1 & 2 & 3 \\ 3 & 1 & 2 \\ 1 & -2 & 4\end{array}\right]$

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Answer

Let $C=\left[\begin{array}{ccc}K-1 & 2 & 3 \\ 3 & 1 & 2 \\ 1 & -2 & 4\end{array}\right]$
Since, $C$ is a singular matrix, $|C|=0$
$
\begin{aligned}
& \therefore\left|\begin{array}{crr}
k-1 & 2 & 3 \\
3 & 1 & 2 \\
1 & -2 & 4
\end{array}\right|=0 \\
& \therefore( k -1)(4+4)-2(12-2)+3(-6-1)=0 \\
& \therefore 8 k -8-20-21=0 \\
& \therefore 8 k =49 \\
& \therefore k =\frac{49}{8}
\end{aligned}
$

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