Further MathematicsCode 9231
Matrices
What this topic asks you to be able to do
- carry out the operations of adding, subtracting and multiplying matrices, and identify the zero matrix and the identity (or unit) matrix
- state what is meant by 'singular' and 'non-singular' when these describe square matrices, and, for 2×2 and 3×3 matrices, evaluate determinants and obtain the inverses of non-singular matrices
- understand the rule (AB)⁻¹ = B⁻¹A⁻¹ for matrices that are non-singular, and use it
- understand how 2×2 matrices can stand for some geometric transformations of the x-y plane, and in particular: understand how the transformations given by A and A⁻¹ are related; recognise that the product AB stands for doing the transformation given by B first and then the one given by A; recall the link between a transformation's area scale factor and the determinant of its matrix; find the matrix for a given transformation or for a sequence of transformations
- know what 'invariant' signifies for points and lines when transformations are described by matrices, and solve simple questions on invariant points and invariant lines