## All Linear Transformations that Take the Line $y=x$ to the Line $y=-x$

## Problem 454

Determine all linear transformations of the $2$-dimensional $x$-$y$ plane $\R^2$ that take the line $y=x$ to the line $y=-x$.

Add to solve laterDetermine all linear transformations of the $2$-dimensional $x$-$y$ plane $\R^2$ that take the line $y=x$ to the line $y=-x$.

Add to solve laterProve that every plane in the $3$-dimensional space $\R^3$ that passes through the origin is a subspace of $\R^3$.

Add to solve later