Question

If A = ${\displaystyle \left[\begin{array}{ccc}1& 2& 3\\ 2& k& 2\\ 5& 7& 3\end{array}\right]}$ is a singular matrix then find the value of 'k'.

Answer 1

A = ${\displaystyle \left[\begin{array}{ccc}1& 2& 3\\ 2& k& 2\\ 5& 7& 3\end{array}\right]}$

As A is a singular matrix.
|A| = o

${\displaystyle \left|\begin{array}{ccc}1& 2& 3\\ 2& k& 2\\ 5& 7& 3\end{array}\right|}$ = o

1(3k - 14) - 2(6 - 10) + 3(14 - 5k) = 0
3k - 14 + 8 + 42 - 15k = o
${\displaystyle \therefore }$ -12k + 36 = 0
${\displaystyle \therefore }$ -12k = -36
${\displaystyle \therefore k=\frac{-36}{-12}}$
k = 3