$\left[\begin{array}{ccc}\mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{p} & \mathbf{q} & \mathbf{r} \\ \mathbf{2 a - p} & \mathbf{2 b}-\mathbf{q} & \mathbf{2 c}-\mathbf{r}\end{array}\right]$
$\therefore \quad|A|=\left|\begin{array}{ccc}a & b & c \\ p & q & r \\ 2 a-p & 2 b-q & 2 c-r\end{array}\right|$
Applying $R_3 \rightarrow R_3+R_2$, wé get$|A|=\left|\begin{array}{ccc}a & b & c \\ p & q & r \\ 2 a & 2 b & 2 c\end{array}\right|$
Taking 2 common from $R_3$, we get
$|A|=2\left|\begin{array}{lll}a & b & c \\ p & q & r \\ a & b & c\end{array}\right|$
$=2(0) \quad \ldots\left[\because R_1\right.$ and $R_3$ are identical $]$
$=0$
$\therefore \quad$ A is a singular matrix.
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