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

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

{\displaystyle {\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 ${\displaystyle P}$ is ${\displaystyle L}$ (that is the set of all outputs is the line ${\displaystyle L}$ when all points on the plane ${\displaystyle P}$ are taken as inputs).