Let $A=\left(\begin{array}{lll}1 & 0 & 0 \ 2 & 1 & 0 \ 3 & 2 & 1\end{array} ight)$. If $u_1$ and $u_2$ are column matrices such that $A u_1=\left(\begin{array}{l}1 \ 0 \ 0\end{array} ight)$ and $A u_2=\left(\begin{array}{l}0 \ 1 \ 0\end{array} ight)$, then $u_1+u_2$ is equal to

Question

Let $A=\left(\begin{array}{lll}1 & 0 & 0 \ 2 & 1 & 0 \ 3 & 2 & 1\end{array}ight)$. If $u_1$ and $u_2$ are column matrices such that $A u_1=\left(\begin{array}{l}1 \ 0 \ 0\end{array}ight)$ and $A u_2=\left(\begin{array}{l}0 \ 1 \ 0\end{array}ight)$, then $u_1+u_2$ is equal to

Aicharya · Accepted Answer

$A=\left(\begin{array}{lll}1 & 0 & 0 \ 2 & 1 & 0 \ 3 & 2 & 1\end{array}ight)$ Let $u_1=\left[\begin{array}{l}a \ b \ c\end{array}ight] ; u_2=\left[\begin{array}{l}d \ e \ f\end{array}ight]$ $\mathrm{Au}_1=\left[\begin{array}{l}1 \ 0 \ 0\end{array}ight] \quad \Rightarrow u_1=\left[\begin{array}{c}1 \ -2 \ 1\end{array}ight]$ $\mathrm{Au}_2=\left[\begin{array}{l}0 \ 1 \ 0\end{array}ight] \quad \Rightarrow \mathrm{u}_2=\left[\begin{array}{c}0 \ 1 \ -2\end{array}ight] \quad \Rightarrow \mathrm{u}_1+\mathrm{u}_2=\left[\begin{array}{c}1 \ -1 \ -1\end{array}ight]$

Let $A=\left(\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right)$. If $u_1$ and $u_2$…

Solution