Question

State whether the following statement is true or false.

The matrix $\left[\begin{array}{ccc}1& 3& 0\\ 4& 0& -2\\ 2& 6& 0\end{array}\right]$ is singular matrix.

• A. True
• B. False

Answer 1

The correct option is A True

Let $A=$ $\left[\begin{array}{ccc}1& 3& 0\\ 4& 0& -2\\ 2& 6& 0\end{array}\right]$

Now,

$|A|$$=\left|\begin{array}{ccc}1& 3& 0\\ 4& 0& -2\\ 2& 6& 0\end{array}\right|$

$=-2(1\times 6-2\times 3)$ [ Expanding about the second row]

$=0$.

So the given matrix $A$ is singular.