(i'd really appreciate if someone fixed the notation, i have no clue how to do it. thanks)
You are given this information at the start of the question:
Really stuck on this, i have no clue what to do so i cant really give you any additional information. I would really appreciate your help. Thank you
Just apply $P_{B\to G}$ to $x_B$: $x_G =P_{B\to G}(x_B) =\begin{pmatrix}1\cdot2+2\cdot(-7)+(-1)\cdot(-10)\\(-2)\cdot2+1\cdot(-7)+0\cdot(-10)\\ 0\cdot2+1\cdot(-7)+1\cdot(-10)\end{pmatrix}=\begin{pmatrix}-2\\-11\\-17\end{pmatrix}$