If $A=\left[\begin{array}{ccccc}0 & 1 & 2 & 3 & 4 \ 0 & 2 & 4 & 8 & 12 \ 0 & 0 & 0 & 4 & 8\end{array} ight]$, then the rank of $A$ is

Question

If $A=\left[\begin{array}{ccccc}0 & 1 & 2 & 3 & 4 \ 0 & 2 & 4 & 8 & 12 \ 0 & 0 & 0 & 4 & 8\end{array}ight]$, then the rank of $A$ is

Aicharya · Accepted Answer

$A=\left[\begin{array}{lllll}0 & 1 & 2 & 3 & 4 \ 0 & 2 & 4 & 8 & 12 \ 0 & 0 & 0 & 4 & 8\end{array}ight]$ $\mathrm{R}_2 ightarrow \mathrm{R}_2-2 \mathrm{R}^1$ $\begin{aligned} & \sim\left[\begin{array}{lllll}0 & 1 & 2 & 3 & 4 \ 0 & 0 & 0 & 2 & 4 \ 0 & 0 & 0 & 4 & 8\end{array}ight] \ & \because\left|\begin{array}{cc}3 & 4 \ 2 & 4\end{array}ight|=12-8=4 \uparrow 0\end{aligned}$ $	herefore$ Rank $=2$

If $A=\left[\begin{array}{ccccc}0 & 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 8 & 12 \\ 0 & 0 & 0 & 4 &…

Solution