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Q.
For what value of x, A = $\left[\begin{matrix}2\left(x+1\right)&2x\\ x&x-2\end{matrix}\right] $ is a singular matrix?
Determinants
Solution:
It is given that $A$ is a singular matrix.
$\therefore \quad\left|A\right|=0$
$\Rightarrow \quad\left|\begin{matrix}2\left(x+1\right)&2x\\ x&x-2\end{matrix}\right|=0\quad\Rightarrow \quad2\left(x+1\right)\left(x-2\right)-2x^{2}=0$
$\Rightarrow \quad2x^{2}-2x-4-2x^{2}=0 \quad\Rightarrow \quad2x+4=0 \, \Rightarrow \, x=-2\qquad\qquad$