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 \(\mathbf{A}\).

Addition and subtraction of matrices.
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.

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