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

${\begin{aligned}&P:x+y+z=1\\&L:u{\begin{bmatrix}1\\1\\1\end{bmatrix}}\quad u\in \mathbb {R} .\end{aligned}}$

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).