Question
Which of the following matrices are singular or non-singular?
$\left[\begin{array}{ccc}5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105\end{array}\right]$
$\left[\begin{array}{ccc}5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105\end{array}\right]$
$\therefore|A|=\left|\begin{array}{ccc}5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105\end{array}\right|$
Applying $\mathrm{C}_2 \rightarrow \mathrm{C}_2+\mathrm{C}_1$
$|A|=\left|\begin{array}{ccc}5 & 5 & 5 \\ 1 & 100 & 100 \\ 6 & 105 & 105\end{array}\right|$
$=0 \ldots\left[\because C_2\right.$ and $C_3$ are identical $]$
∴ A is a singular matrix.
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