← Further Maths syllabus

EnglandFurther Maths

Core Pure: matrices and transformations

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you find the inverse of a 2x2 and 3x3 matrix, and when does an inverse exist?

The inverse of a 2x2 matrix, the existence condition (non-zero determinant), the inverse of a 3x3 matrix via the adjugate or row reduction, and the inverse of a product.
A focused answer to the OCR A-Level Further Mathematics A content on inverse matrices, covering the formula for the inverse of a 2x2 matrix, the condition for an inverse to exist, finding the inverse of a 3x3 matrix using the adjugate (matrix of cofactors) or row reduction, and the rule for the inverse of a product of matrices.
12 min answer →

How do matrices represent geometric transformations of the plane and of space, and how do you compose and reverse them?

Matrices as linear transformations in two and three dimensions (rotations, reflections, enlargements, stretches and shears), composition by multiplication, invariant points and lines, and the determinant as an area or volume scale factor.
A focused answer to the OCR A-Level Further Mathematics A content on matrices as linear transformations, covering the standard matrices for rotations, reflections, enlargements, stretches and shears in two and three dimensions, composing transformations by matrix multiplication, finding invariant points and invariant lines, and reading the determinant as an area or volume scale factor.
12 min answer →

How do you add, multiply and take the determinant of matrices, and what does the determinant tell you geometrically?

Matrix addition, subtraction, scalar multiplication and multiplication, the zero and identity matrices, non-commutativity, and the determinant of a 2x2 and 3x3 matrix as an area or volume scale factor.
A focused answer to the OCR A-Level Further Mathematics A content on matrix arithmetic and determinants, covering addition, subtraction and scalar multiplication, matrix multiplication and its non-commutativity, the zero and identity matrices, and the determinant of a 2x2 and 3x3 matrix interpreted as an area or volume scale factor.
11 min answer →

How do you use matrices to solve a system of linear equations, and how do you interpret the geometry when the determinant is zero?

Writing a system of linear equations as a matrix equation, solving by the inverse matrix, and the geometric interpretation of consistent, inconsistent and dependent systems in two and three unknowns.
A focused answer to the OCR A-Level Further Mathematics A content on solving systems of linear equations with matrices, covering how to write a system as a matrix equation, solving by multiplying by the inverse, and interpreting the geometry of two or three planes when the determinant is non-zero (a unique point), zero with consistency (a line, a sheaf) or zero with inconsistency (no solution).
11 min answer →