Answer
$[x]_B=\begin{bmatrix}
2\\
-1\\
\end{bmatrix}
$
$[y]_B=\begin{bmatrix}
3/2\\
1\\
\end{bmatrix}
$
$[z]_B=\begin{bmatrix}
-1\\
-1/2\\
\end{bmatrix}
$
Work Step by Step
We can calculate the B coordinate vector of x by row reducing the augmented matrix
$\begin{bmatrix}
0&2&-2\\
2&1&3\\
\end{bmatrix}
$~$\begin{bmatrix}
1&0&2\\
0&1&-1\\
\end{bmatrix}$
We can calculate the B coordinate vector of y by row reducing the augmented matrix
$\begin{bmatrix}
0&2&2\\
2&1&4\\
\end{bmatrix}
$~$\begin{bmatrix}
1&0&3/2\\
0&1&1\\
\end{bmatrix}$
We can calculate the B coordinate vector of z by row reducing the augmented matrix
$\begin{bmatrix}
0&2&-1\\
2&1&-2.5\\
\end{bmatrix}
$~$\begin{bmatrix}
1&0&-1\\
0&1&-1/2\\
\end{bmatrix}$
