Chapter 4.2, Problem 4E

Let L be the linear operators on ${ℝ}^3$ defined by

$L(x)=\left[\begin{array}{c}2x_1-x_2-x_3\\ 2x_2-x_1-x_3\\ 2x_3-x_1-x_2\end{array}\right]$

Determine the standard matrix representation A of L, and use A to find $L(x)$ for each of the following vectors x:

(a) $x={(1,1,1)}^T$

(b) $x={(2,1,1)}^T$

(c) $x={(-5,3,2)}^T$