Question

If \[A=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\] and \[B=\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\], find \[2A-B\].

Options

• \[\begin{bmatrix}1&-5&-3\\-5&-6&0\end{bmatrix}\]

• \[\begin{bmatrix}-1&5&3\\5&6&0\end{bmatrix}\]

• \[\begin{bmatrix}5&3&9\\3&6&4\end{bmatrix}\]

• \[\begin{bmatrix}-1&3&3\\3&6&4\end{bmatrix}\]

Answer 1

First, \[2A=\begin{bmatrix}2&4&6\\4&6&2\end{bmatrix}\]. Then use \[2A-B=2A+(-B)\]. Adding corresponding entries gives \[\begin{bmatrix}-1&5&3\\5&6&0\end{bmatrix}\].