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

Question

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

Aicharya · Accepted Answer

Let $A$ $ \begin{aligned} =\left[\begin{array}{ccc} 1 & 0 & 2 \ 0 & 1 & -2 \ 1 & -1 & 4 \ 2 & 2 & 8 \end{array}ight] & \sim\left[\begin{array}{ccc} 1 & 0 & 2 \ 0 & 1 & -2 \ 0 & -1 & 2 \ 0 & 2 & 4 \end{array}ight]\left[R_3 ightarrow R_3-R_1 ; R_4 ightarrow R_4-2 R_1ight] \ & \sim\left[\begin{array}{ccc} 1 & 0 & 2 \ 0 & 1 & -2 \ 0 & 0 & 0 \ 0 & 0 & 8 \end{array}ight]\left[R_3 ightarrow R_3+R_2 ; R_4 ightarrow R_4-2 R_2ight] \end{aligned} $ Number of non-zero rows is 3 $	herefore$ Rank of $A=3$

The rank of the matrix $\left[\begin{array}{ccc}1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 &…

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