Question

If $A=\left[\begin{array}{ccc}0& x& 16\\ x& 5& 7\\ 0& 9& x\end{array}\right]$ is singular, then the possible values of $x$ are

• A. $0,\pm 1$
• B. $0,\pm 12$
• C. $0,\pm 5$
• D. $0,\pm 4$

Answer 1

Answer: (B)

$0,\pm 12$

$\begin{array}{c}Singularmeans\\ \left|A\right|=0\\ \left(\begin{array}{ccc}0& x& 16\\ x& 5& 7\\ 0& 9& x\end{array}\right)=0\\ 0\left(51-63\right)-x\left(x^2\right)+16\left(9x\right)=0\\ -x^3+144x=0\\ x^{3‘}-144x=0\\ x\left(x^2-144\right)=0\\ x=0\\ x^2-144=0\\ x^2=144\\ x=\pm 12\\ x=0,\pm 12\end{array}$

Hence, this is the answer.