Question

Can someone please help me with this? Thank you!

Answer 1

`\left[\begin{array}{ccc}-25&(75)/(2)&-(25)/(2)\end{array}\right]`

Explanation:

In the first equality

`5* \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =(2)/(5)m* \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=(2)/(5)m\Rightarrow m=5* (5)/(2)=(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* H=(25)/(2)* [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&(75)/(2)&-(25)/(2)\end{array}\right]`