Question

The rank of matrix $\left[\begin{array}{ccc}1& 2& -1\\ 2& 4& 6\\ 0& 0& -8\end{array}\right]$ is

• A. 2
• B. 1
• C. 3
• D. None of the above

Answer 1

The correct option is A 2

A = $\left[\begin{array}{ccc}1& 2& -1\\ 2& 4& 6\\ 0& 0& -8\end{array}\right]$

$R_2\to R_2-2R_1$

$\sim \left[\begin{array}{ccc}1& 2& -1\\ 0& 0& 8\\ 0& 0& -8\end{array}\right]$

$R_3\to R_3+R_2$

$\sim \left[\begin{array}{ccc}1& 2& -1\\ 0& 0& 8\\ 0& 0& 0\end{array}\right]$

$\Rightarrow Rank\left(A\right)=2$