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Question
If A =`[[2 3],[5 7]],B =` `[[-1 0 2],[3 4 1]]`,`C= [[-1 2 3],[2 1 0]]`find
2B + 3A and 3C − 4B
Solution
`2B +3A=2[[-1 0 2],[3 4 1]]``+3[[2 3],[5 7]]`
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.
\[ \Rightarrow 3C - 4B = 3\begin{bmatrix}- 1 & 2 & 3 \\ 2 & 1 & 0\end{bmatrix} - 4\begin{bmatrix}- 1 & 0 & 2 \\ 3 & 4 & 1\end{bmatrix}\]
\[ \Rightarrow 3C - 4B = \begin{bmatrix}- 3 & 6 & 9 \\ 6 & 3 & 0\end{bmatrix} - \begin{bmatrix}- 4 & 0 & 8 \\ 12 & 16 & 4\end{bmatrix}\]
\[ \Rightarrow 3C - 4B = \begin{bmatrix}- 3 + 4 & 6 - 0 & 9 - 8 \\ 6 - 12 & 3 - 16 & 0 - 4\end{bmatrix}\]
\[ \Rightarrow 3C - 4B = \begin{bmatrix}1 & 6 & 1 \\ - 6 & - 13 & - 4\end{bmatrix}\]
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