Question

For what value of $x$ the matrix $A$ is singular

$\left[\begin{array}{cc}1+x& 7\\ 3-x& 8\end{array}\right]$

Answer 1

Calculate the value of $x$:

We know that a matrix is singular when its determinant is $0$.

If $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is a matrix then its determinant is given as

$D=ad-bc$

The given matrix is $\left[\begin{array}{cc}1+x& 7\\ 3-x& 8\end{array}\right]$.

$\therefore D=0$

$\Rightarrow \left(1+x\right)8-7\left(3-x\right)=0$

$\Rightarrow$ $8+8x-21+7x=0$

$\Rightarrow$ $15x=13$

$\Rightarrow$ $x=\frac{13}{15}$

Hence, the value of $x$ is $\frac{13}{15}$.