Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 30/Statement

Let $P$ be a plane and $L$ a line in ${\mathbb{ℝ}}^3$ given by equations

$\begin{array}{rl}& P:x+y+z=1\\ & L:u\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]u\in \mathbb{ℝ}.\end{array}$

Find all linear transformations such that the image of $P$ is $L$ (that is the set of all outputs is the line $L$ when all points on the plane $P$ are taken as inputs).