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# For what value of x, the matrix $\begin{bmatrix} 5-x & x+1 \\ 2 & 4 \end{bmatrix}$ is singular?

Toolbox:
• If matrix A is singular then $\mid A\mid=0$
Step 1:
Let $A=\begin{bmatrix}5-x&x+1\\2&4\end{bmatrix}$
If matrix A is singular then
$\mid A\mid=\begin{vmatrix}5-x&x+1\\2&4\end{vmatrix}=0$
Step 2:
On expanding we get,
$(5-x)4-2(x+1)=0$
$20-4x-2x-2=0$
$-6x+18=0$
$\Rightarrow x=3$