Question

Find the rank of the matrix $\left[\begin{array}{cccc}4& 2& 1& 3\\ 6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$

Answer 1

Given matrix is $\left[\begin{array}{cccc}4& 2& 1& 3\\ 6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$

Do operation $R_2=R_2-R_1-R_3$ , we get $\left[\begin{array}{cccc}4& 2& 1& 3\\ 0& 0& 3& 3\\ 2& 1& 0& 1\end{array}\right]$

Now do operation $R_1=R_1-2R_3$ , we get $\left[\begin{array}{cccc}0& 0& 1& 1\\ 0& 0& 3& 3\\ 2& 1& 0& 1\end{array}\right]$

Now do operation $R_2=R_2-3R_1$ , we get $\left[\begin{array}{cccc}0& 0& 1& 1\\ 0& 0& 0& 0\\ 2& 1& 0& 1\end{array}\right]$

Therefore the rank of matrix is $2$