Tagged: reflection

The Matrix for the Linear Transformation of the Reflection Across a Line in the Plane

Problem 498

Let $T:\R^2 \to \R^2$ be a linear transformation of the $2$-dimensional vector space $\R^2$ (the $x$-$y$-plane) to itself which is the reflection across a line $y=mx$ for some $m\in \R$.

Then find the matrix representation of the linear transformation $T$ with respect to the standard basis $B=\{\mathbf{e}_1, \mathbf{e}_2\}$ of $\R^2$, where
1 \\
\end{bmatrix}, \mathbf{e}_2=\begin{bmatrix}
0 \\

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