Transformations (AQA A-Level Further Maths): Flashcards

Transformation represented by a matrix

Matrix on left: $\mathbf{T}\mathbf{x}$, not $\mathbf{x}\mathbf{T}$

$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$

$\cos$ on diag, $-\sin$ top-right, $\sin$ bottom-left

$\begin{pmatrix} k & 0 \\ 0 & k \end{pmatrix}$

$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

Columns show where basis vectors move to

$\mathbf{A}$ first, then $\mathbf{B}$ (read right to left)

Point where $\mathbf{Tx} = \mathbf{x}$ (stays unchanged)

z-coordinate unchanged, rotation in xy-plane