Question

The rank of the matrix $\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 1& 1\end{array}\right]$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

A = $\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 1& 1\end{array}\right]$

$R_2\to R_2-R_1,R_3\to R_3-R_1$

$\sim \left[\begin{array}{ccc}1& 1& 1\\ 0& -2& -1\\ 0& 0& 0\end{array}\right]$

$\therefore rank\left(A\right)=2$