Question

The rank of the following matrix is

$\left(\begin{array}{cccc}1& 1& 0& -2\\ 2& 0& 2& 2\\ 4& 1& 3& 1\end{array}\right)$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

A = $\left(\begin{array}{cccc}1& 1& 0& -2\\ 2& 0& 2& 2\\ 4& 1& 3& 1\end{array}\right)$ $\underset{R_3\to R_3-4R_1}{\overset{R_2\to R_2-2R_1}{\to }}$

$\left[\begin{array}{cccc}1& 1& 0& -2\\ 0& -2& 2& 6\\ 0& -3& 3& 9\end{array}\right]\stackrel{R_3\to R_3-\frac{3}{2}{R}_2}{\to }\left[\begin{array}{cccc}1& 1& 0& -2\\ 0& -2& 2& 6\\ 0& 0& 0& 0\end{array}\right]$

So $\rho \left(A\right)=2.$