Question

The rank of the matrix $\left[\begin{array}{ccc}-5& 3& 2\\ 3& 2& -5\\ 4& -1& -3\end{array}\right]$ is

• A. $3$
• B. $2$
• C. $1$
• D. none of these

Answer 1

Answer: (B)

$2$

Let $A=\left[\begin{array}{ccc}-5& 3& 2\\ 3& 2& -5\\ 4& -1& -3\end{array}\right]$

Here, $|A|=55-33-22=0$

Hence, the rank of $A<3$
Now, $\left|\begin{array}{cc}-5& 3\\ 3& 2\end{array}\right|=-19\ne 0$

i.e. there is at least one non-zero minor of order 2.

Hence, the rank of $A=2$