Examples
Remember:
Linear transformations in 2d use \(\begin{pmatrix}ax+by \\ cx+dy\end{pmatrix}\)
Exercise 7A: Q2
- \(\begin{pmatrix}2 & -1 \\ 3 & 0\end{pmatrix}\)
- Not a linear transformation by matrix
- \(\cancel{\begin{pmatrix}y & 0 \\ 0 & 0\end{pmatrix} }\) Not a linear transformation by matrix
- \(\begin{pmatrix}0 & 2 \\ -1 & 0\end{pmatrix}\)
- \(\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}\)
Exercise 7A: Q7
- \(\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}2 \\ 1\end{pmatrix}=\begin{pmatrix}-2 \\-1\end{pmatrix}\)
- \(\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}4 \\ 1\end{pmatrix}=\begin{pmatrix}-4 \\ -1\end{pmatrix}\)
- \(\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}4 \\ 2\end{pmatrix}=\begin{pmatrix}-4 \\ -2\end{pmatrix}\)
- \(\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}2 \\ 2\end{pmatrix}=\begin{pmatrix}-2 \\ -2\end{pmatrix}\)
- Rotation 180\(^{\circ}\)