Question

Find the rank of the matrix $\left[\begin{array}{cccc}1& 1& 1& 3\\ 2& -1& 3& 4\\ 5& -1& 7& 11\end{array}\right]$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

$A=\left[\begin{array}{cccc}1& 1& 1& 3\\ 2& -1& 3& 4\\ 5& -1& 7& 11\end{array}\right]R_2\to R_2-2R_1{R}_3\to R_3-5R_1\left[\begin{array}{cccc}1& 1& 1& 3\\ 0& -3& 1& -2\\ 0& -6& 2& -4\end{array}\right]R_3\to R_3-2R_2\left[\begin{array}{cccc}1& 1& 1& 3\\ 0& -3& 1& -2\\ 0& 0& 0& 0\end{array}\right]$

The no. of non-zero row is $2$

So, Rank is $2$.