Question

Can someone please help me with this? Thank you!

Answer 1

Answer:

$\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]$

Step-by-step explanation:

In the first equality

$5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],$

the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so

$5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}$

For the second equality

$(H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),$

if $H=[-2\ 3\ -1]$, then this equality represents the assotiative property of matrix addition.

Hence,

$m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]$