Matrices · Year 13
In Year 13 you learn: multiplying matrices.
A matrix is a rectangular array of numbers. Matrices store data neatly, but their real power is as transformations. Multiplying a vector by a 2 × 2 matrix rotates, reflects, stretches or shears it. Multiplying matrices combines transformations.
Key facts
- Order m × n means m rows and n columns. Add or subtract only matrices of the same order, entry by entry.
- AB exists when the number of columns of A equals the number of rows of B. Entry (i, j) is row i of A times column j of B.
- Usually AB ≠ BA, but (AB)C = A(BC). The identity matrix I leaves everything unchanged.
- Rotation by θ anticlockwise about O: [[cos θ, −sin θ], [sin θ, cos θ]].
Worked examples
Example 1
Find the image of the point (3, 1) after a rotation of 90° anticlockwise about the origin.
Answer: (−1, 3)