Matrices as transformations

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Useful for: IB Math AI HL AP® Precalculus

Learn it A 2 × 2 matrix moves points: multiply it by the point's column vector. [0 −1; 1 0] rotates 90° counterclockwise, [1 0; 0 −1] reflects in the x-axis, [k 0; 0 k] enlarges by k. The determinant gives the area scale factor.

Example: Image of (3, 1) under a 90° rotation?

[0 −1; 1 0][3; 1] = [−1; 3].
(−1, 3).

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