# 1:Find the determinant of the following mattrix [((2,-1,-6)),((-3,0,5)),((4,3,0))] 2: If told that matrix A is singular Matrix find the possible value(s) for x A = { (16x, 4x),(x,9):}

1:Find the determinant of the following mattrix $\left[\begin{array}{c}\begin{array}{ccc}2& -1& -6\end{array}\\ \begin{array}{ccc}-3& 0& 5\end{array}\\ \begin{array}{ccc}4& 3& 0\end{array}\end{array}\right]$

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

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Given:
$A=\left[\begin{array}{ccc}2& -1& -6\\ -3& 0& 5\\ 4& 3& 0\end{array}\right]$
As discussed above determinant of $A=2\left(0-3\cdot 5\right)-\left(-1\right)\left[-3\cdot 0-4\cdot 5\right]+\left(-6\right)\left[-3\cdot 3-4\cdot 0\right]$
$=2\left(-15\right)+1\left(0-20\right)-6\left(-9-0\right)$
$=-30-20+54=4$
Hence, he determinant of the given matrix=4
$c.A=\left[\begin{array}{cc}16x& 4x\\ x& 9\end{array}\right]$
We know when the matrix is single determinant is zero
Calculating the determinant of A
$|A|=16\cdot 9-x\cdot 4x$
$=144-4{x}^{2}$
Now, put $|A|=0$
i.e,
$144-4{x}^{2}=0$
$4{x}^{2}=144$
${x}^{2}=\frac{144}{4}=36$
${x}^{2}=36⇒x=\sqrt{\left(}36\right)$
$x=6$
Hence, $x=-6$ or $x=6$
$\left(-6,=6\right)$