The rank of $\left[\begin{array}{ccc}2 & 1 & 1 \ 0 & 3 & -1 \ 1 & -1 & 1\end{array}\right]$ is

Question

Aicharya · Accepted Answer

$\begin{aligned} & \begin{aligned} A & =\left[\begin{array}{ccc} 2 & 1 & 1 \ 0 & 3 & -1 \ 1 & -1 & 1 \end{array}\right] \ R_3 \rightarrow & 2 R_3-R_1 \ & =\left[\begin{array}{ccc} 2 & 1 & 1 \ 0 & 3 & -1 \ 0 & -3 & 1 \end{array}\right] \ R_3 \rightarrow & R_3+R_2 \ & =\left[\begin{array}{ccc} 2 & 1 & 1 \ 0 & 3 & -1 \ 0 & 0 & 0 \end{array}\right] \end{aligned} \end{aligned}$ $\therefore$ Rank of $A=2$ Hence, option (b) is correct.

The rank of \(\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]\) is

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