# Matrix Algebra – Edexcel FP1

#### 4. Matrix Algebra – Edexcel Further Pure Mathematics 1 (FP1)

What students need to learn:
Linear transformations of column vectors in two dimensions and their matrix representation.
The transformation represented by $$\mathbf{AB}$$ is the transformation represented by $$\mathbf{B}$$ followed by the transformation represented by $$\mathbf{A}$$.

Multiplication of a matrix by a scalar.
Products of matrices.

Evaluation of $$2 × 2$$ determinants.
Singular and non-singular matrices.

Inverse of $$2 × 2$$ matrices.
Use of the relation
$$(\mathbf{AB})^{–1} = \mathbf{B}^{–1} \mathbf{A}^{–1}$$.

Combinations of transformations.
Applications of matrices to geometrical transformations.

Identification and use of the matrix representation of single and combined transformations from: reflection in coordinate axes and lines $$y = \pm x$$, rotation of multiples of 45° about (0, 0) and enlargement about centre (0, 0), with scale factor, $$(k \neq 0)$$, where $$k \in \mathbb{R}$$.

The inverse (when it exists) of a given transformation or combination of transformations.
Idea of the determinant as an area scale factor in transformations.