Question

(4) Determine the values of a and so that the following matrices are singular:
A=(7 3
-2 a)
​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

A Matrix B is said to be singular if

det B = |B| = 0

Now it is given that

$\displaystyle \: A = \displaystyle\begin{pmatrix} \: \: \: 7 & \: 3\\ - 2 & \: a \end{pmatrix} </strong><strong>$

Now

$| A | </strong></p><p><strong>= \displaystyle\begin{vmatrix} \: \: \: 7 & 3 \\ - 2 & a \end{vmatrix} = (7 \times a) - ( - 2 \times 3) = 7a + 6</strong></p><p><strong>$

Since A is singular

So

$\displaystyle \: 7a + 6 = 0$

$\implies \: a \: = - \frac{6}{7}$