Chapter 4.3, Problem 3E

Let L be the linear transformation on ${ℝ}^3$ defined by
$L(x)=\left[\begin{array}{c}2x_1-x_2-x_3\\ 2x_2-x_1-x_3\\ 2x_3-x_1-x_2\end{array}\right]$
and let A be the standard matrix representation of L (see Exercise 4 of Section 4.2). If $u_1={(1,1,0)}^T$ , $u_2={(1,0,1)}^T$and $u_3={(0,1,1)}^T$ , then $\{u_1,u_2,u_3\}$ is an ordered basis for ${ℝ}^3$ and $U=(u_1,u_2,u_3)$ is the transition matrix corresponding to a change of basis from $\{u_1,u_2,u_3\}$ to the standard basis $\{e_1,e_2,e_3\}$ . Determine the matrix B representing L with respect to the basis $\{u_1,u_2,u_3\}$ by calculating $U^{-1}AU$ .