Question

The rank of the matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 3& 6& 9\\ 1& 2& 3\end{array}\right]$, is

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

Answer 1

The correct option is A 1

$A=\left[\begin{array}{ccc}1& 2& 3\\ 3& 6& 9\\ 1& 2& 3\end{array}\right]$
Here, $|A|=0$
So, rank of$A<3$
Here, $R_1$ and $R_3$ rows are identical. Also $R_2$ is proportional to $R_1$
Therefore, rank $=1$
Hence, option 'A' is correct.