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Examples

Remember:

Linear transformations in 2d use \(\begin{pmatrix}ax+by \\ cx+dy\end{pmatrix}\)

Exercise 7A: Q2
  1. \(\begin{pmatrix}2 & -1 \\ 3 & 0\end{pmatrix}\)
  2. Not a linear transformation by matrix
  3. \(\cancel{\begin{pmatrix}y & 0 \\ 0 & 0\end{pmatrix} }\) Not a linear transformation by matrix
  4. \(\begin{pmatrix}0 & 2 \\ -1 & 0\end{pmatrix}\)
  5. \(\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}\)
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\(^{\circ}\)
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