Question
If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find2B + 3A and 3C - 4B.
✓
Answer
$2\text{B}+3\text{A}=2\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}+3\begin{bmatrix}2&3\\5&7\end{bmatrix}$
It is not possible to add these matrices because the number of elements in B are not equal to the number of elements in A. So, 2B + 3A does not exist.
$\Rightarrow3\text{C}-4\text{B}=3\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix}-4\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3&6&9\\6&3&0\end{bmatrix}-\begin{bmatrix}-4&0&8\\12&16&4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3+4&6-0&9-8\\6-12&3-16&0-4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}1&6&1\\-6&-13&-4\end{bmatrix}$
It is not possible to add these matrices because the number of elements in B are not equal to the number of elements in A. So, 2B + 3A does not exist.
$\Rightarrow3\text{C}-4\text{B}=3\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix}-4\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3&6&9\\6&3&0\end{bmatrix}-\begin{bmatrix}-4&0&8\\12&16&4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3+4&6-0&9-8\\6-12&3-16&0-4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}1&6&1\\-6&-13&-4\end{bmatrix}$
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