If told that matrix A is a singular Matrix find the possible value(s) for x...

Tammy Todd

Answered question

2021-10-20

If told that matrix A is a singular Matrix find the possible value(s) for x $A=\left[\begin{array}{cc}16& 4x\\ x& 9\end{array}\right]$

Answer & Explanation

Clelioo

Skilled2021-10-21Added 88 answers

Step 1
If A is a singular matrix, then $det\left(A\right)=0$ $\Rightarrow \left[\begin{array}{cc}16& 4x\\ x& 9\end{array}\right]=0$ $\Rightarrow 16\left(9\right)-4{x}^{2}=0$ $\Rightarrow -4({x}^{2}-36)=0$ $\Rightarrow {x}^{2}-36$ $\therefore x=\pm 6$
Therefore for $x=-6,\text{}6$ the matrix A is singular.