Chapter 4.2, Problem 6E

Let

$b_1=\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right],b_2=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right],b_3=\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right]$

and let L be the linear transformation from ${ℝ}^2$ into ${ℝ}^3$ defined by

$L(x)=x_1{b}_1+x_2{b}_2+(x_1+x_2)b_3$

Find the matrix A representing L with respect to the ordered bases $\left\{e_1,e_2\right\}$ and $\left\{b_1,b_2,b_3\right\}$ .