Question

The value of x for which the matrix $A=\left[\begin{array}{ccc}3& 2& 4\\ 9& 7& 13\\ -6& -4& -9+x\end{array}\right]$ has zero as an eigen value is ______ .

• A. 1

Answer 1

The correct option is A 1
Matrix A = $\left[\begin{array}{ccc}3& 2& 4\\ 9& 7& 13\\ -6& -4& -9+x\end{array}\right]$

eigen value of matrix A = 0

$\Rightarrow$ determinant(A) = 0

Hence, |A| = 0

$\Rightarrow 3\left[7\right(-9+x)-(-4\left)\right(13\left)\right]-2\left[9\right(-9+x)-(13\left)\right(-6\left)\right]+4\left[9\right(-4)-(-6\left)\right(7\left)\right]=0$

$\Rightarrow 3[-63+7x+52]-2[-81+9x+78]+4[-36+42]=0$

$\Rightarrow -33+21x+6-18x+24=0$

$\Rightarrow -3+3x=0$

$\Rightarrow 3x=3$

$\Rightarrow x=1$