The book said to use equation 6, but I don’t know how it applies.  When I tried to apply equation 6, I kept getting the wrong answer.  Could you please walk me through this problem?  Thanks!

$\begin{bmatrix} 1 \\ 0 \end{bmatrix}=\frac{1}{2}\left(\,\begin{bmatrix} 1 \\ 1 \end{bmatrix}+\begin{bmatrix} 1 \\ -1 \end{bmatrix}\,\right)$ $\begin{bmatrix} 0 \\ 1 \end{bmatrix}=\frac{1}{2}\left(\,\begin{bmatrix} 1 \\ 1 \end{bmatrix}-\begin{bmatrix} 1 \\ -1 \end{bmatrix}\,\right).$ Find $T\left(\, \begin{bmatrix} 1 \\ 0 \end{bmatrix} \,\right)$ and $T\left(\, \begin{bmatrix} 0 \\ 1 \end{bmatrix} \,\right)$ and write $T\left(\, \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \,\right)$ as a linear combination of these two.
Different methods to solve this kind of problems are explained in Find a general formula of a linear transformation from $\R^2$ to $\R^3$