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

Answer 1

`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.

\[ \Rightarrow 3C - 4B = 3\begin{bmatrix}- 1 & 2 & 3 \\ 2 & 1 & 0\end{bmatrix} - 4\begin{bmatrix}- 1 & 0 & 2 \\ 3 & 4 & 1\end{bmatrix}\]

\[ \Rightarrow 3C - 4B = \begin{bmatrix}- 3 & 6 & 9 \\ 6 & 3 & 0\end{bmatrix} - \begin{bmatrix}- 4 & 0 & 8 \\ 12 & 16 & 4\end{bmatrix}\]

\[ \Rightarrow 3C - 4B = \begin{bmatrix}- 3 + 4 & 6 - 0 & 9 - 8 \\ 6 - 12 & 3 - 16 & 0 - 4\end{bmatrix}\]

\[ \Rightarrow 3C - 4B = \begin{bmatrix}1 & 6 & 1 \\ - 6 & - 13 & - 4\end{bmatrix}\]