Question

The rank of the matrix $\left[\begin{array}{cccc}4& 1& 0& 0\\ 3& 0& 1& 0\\ 5& 0& 0& 1\end{array}\right]$ is

• A. $4$
• B. $3$
• C. $2$
• D. none of these

Answer 1

The correct option is B $3$

Given, $A=\left[\begin{array}{cccc}4& 1& 0& 0\\ 3& 0& 1& 0\\ 5& 0& 0& 1\end{array}\right]$
Rank of $A$ is $min3$
Rank of A $\le 3$
Now, $\left|\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right|=1\ne 0$
i.e there is at least one non-zero minor of order 3.
Hence, rank of A =3