Question

For what value of $x$ the given matrix $A=\left[\begin{array}{cc}3-2x& x+1\\ 2& 4\end{array}\right]$ is singular matrix.

Answer 1

$A=\left(\begin{array}{cc}3x-2& x+1\\ 2& 4\end{array}\right)$

$forsingularmatrix,detarminantofAshouldbezeroi.e,\left|A\right|=0$

Therefore,

$\left(3x-2\right)\times 4-2\left(x+1\right)=012x-8-2x-2=010x-10=010x=10x=1$

Hence, this is the answer.