- #1
flyingpig
- 2,579
- 1
Homework Statement
Find the standard matrix of T
[tex]T: \mathbb{R}^2 \to \mathbb{R}^2 [/tex] first performs a horizontal shear tha transforms e2 into e2 - 2e1 (leaving e1) unchanged) and then reflects points through the line x2 = x1
The Attempt at a Solution
[tex]e_1 = \begin{bmatrix}
1\\
0
\end{bmatrix}[/tex]
[tex]e_2 = \begin{bmatrix}
0\\
1
\end{bmatrix}[/tex]
[tex]e_2 - 2e_1 = \begin{bmatrix}
2\\
1
\end{bmatrix}[/tex]
[tex]A= \begin{bmatrix}
-2 & 1 \\
1 & 0
\end{bmatrix}[/tex]
Now I am completely stuck, how do I do the reflection? I know the standard matrix is just
A= [tex]\begin{bmatrix}
0 & -1 \\
-1 & 0
\end{bmatrix}[/tex]
But how do I "add" this information to my old standard matrix?