Question

Rank of the matrix $\left[\begin{array}{ccc}0& 2& 2\\ 7& 4& 8\\ -7& 0& -4\end{array}\right]$ is 3

• A. True
• B. False

Answer 1

The correct option is B False

$\left[\begin{array}{ccc}0& 2& 2\\ 7& 4& 8\\ -7& 0& -4\end{array}\right]$$\stackrel{R_{2\to R_2}-2R_1}{\to }$$\left[\begin{array}{ccc}0& 2& 2\\ 7& 0& 4\\ -7& 0& -4\end{array}\right]$

$\stackrel{R_3\to R_3+R_2}{\to }$ $\left[\begin{array}{ccc}0& 2& 2\\ 7& 0& 4\\ 0& 0& 0\end{array}\right]\stackrel{R_1\leftarrow R_2}{\to }\left[\begin{array}{ccc}7& 0& 4\\ 0& 2& 2\\ 0& 0& 0\end{array}\right]$

$\therefore$ Rank of matrix = 2