Question

Let A =$\left \lgroup\begin{array}{ccc}1&0&0\\2&1&0\\3&2&1\end{array}\right\rgroup$. If u₁ and u₂ are column matrices such that Au₁ = $\left \lgroup\begin{array}{c}1\\0\\0\end{array}\right \rgroup$ and Au₂ = $\left\lgroup\begin{array}{c}0\\1\\0\end{array}\right\rgroup$, then u₁ + u₂ is equal to :
(a) $\left\lgroup\begin{array}{c}-1\\1\\0\end{array}\right\rgroup$(b) $\left\lgroup\begin{array}{c}-1\\1\\-1\end{array}\right\rgroup$(c) $\left\lgroup\begin{array}{c}-1\\-1\\0\end{array}\right\rgroup$(d) $\left\lgroup\begin{array}{c}1\\-1\\-1\end{array}\right\rgroup$

Answer 1

and u₂ are column matrices such that Au₁ = $\left \lgroup\begin{array}{c}1\\0\\0\end{array}\right \rgroup$ and Au₂ = $\left\lgroup\begin{array}{c}0\\1\\0\end{array}\right\rgroup$, then u₁ + u₂ is equal to :

(a) $\left\lgroup\begin{array}{c}-1\\1\\0\end{array}\right\rgroup$(b) $\left\lgroup\begin{array}{c}-1\\1\\-1\end{array}\right\rgroup$(c) $\left\lgroup\begin{array}{c}-1\\-1\\0\end{array}\right\rgroup$(d) $\left\lgroup\begin{array}{c}1\\-1\\-1\end{array}\right\rgroup$