"Solution 3 question 10A
Why in the question said that [x]B=(-1,3)^T but your solution you write [x]B’=(-1,3) how does it change?"

It is the same thing:

[x]B' = (-1,3)^T = -1

                             3

This is the definition of transpose.

There is also another post discussing the flexibility in writing column vectors as row vectors. It is ok to interchange a row and column since they contain the same information as long as you are not doing matrix multiplication.

If you are doing matrix multiplication then you must write it in the correct form.

In this question, the I have not altered the form. The ^T transposes it so the row appears as a column.