A) \[\left( \begin{align} & -1 \\ & 1 \\ & 0 \\ \end{align} \right)\]
B) \[\left( \begin{align} & -1 \\ & 1 \\ & -1 \\ \end{align} \right)\]
C) \[\left( \begin{align} & -1 \\ & -1 \\ & 0 \\ \end{align} \right)\]
D) \[\left( \begin{align} & 1 \\ & -1 \\ & -1 \\ \end{align} \right)\]
Correct Answer: D
Solution :
\[A({{u}_{1}}+{{u}_{2}})=\left( \begin{align} & 1 \\ & 1 \\ & 0 \\ \end{align} \right)\] \[\left| A \right|=1\] \[{{A}^{-1}}=\frac{1}{\left| A \right|}adj\,\,A\] \[{{u}_{1}}+{{u}_{2}}={{A}^{-1}}\left[ \begin{align} & 1 \\ & 1 \\ & 0 \\ \end{align} \right]\] \[{{A}^{-1}}=\left[ \begin{matrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 1 & -2 & 1 \\ \end{matrix} \right]=\left[ \begin{align} & 1 \\ & -1 \\ & -1 \\ \end{align} \right]\]You need to login to perform this action.
You will be redirected in
3 sec