Answer:
[tex]\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]
Step-by-step explanation:
In the first equality
[tex]5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],[/tex]
the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so
[tex]5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}[/tex]
For the second equality
[tex](H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),[/tex]
if [tex]H=[-2\ 3\ -1][/tex], then this equality represents the assotiative property of matrix addition.
Hence,
[tex]m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]
