A matrix is a grid of numbers that describes what a transformation does to the plane — a rotation, a reflection, a stretch. Writing it this way means you can do algebra with transformations: applying one after another becomes multiplication, and undoing one becomes finding an inverse.
Syllabus points covered
- Carry out matrix addition, subtraction and multiplication
- Evaluate determinants of 2×2 and 3×3 matrices and recognise singular matrices
- Find the inverse of a non-singular 2×2 or 3×3 matrix
- Understand the relationship between a matrix and the linear transformation it represents
- Solve systems of linear equations using matrices, and interpret the geometry of the solutions
Common mistakes
- Multiplying matrices in the wrong order — in a composite transformation the first one applied goes on the right.
- Sign errors in the 3×3 determinant expansion; the middle term is subtracted.
- Writing the inverse of a 2×2 without swapping the leading diagonal and negating the other two.
- Treating a zero determinant as an error rather than as information about the transformation.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheet
- Worksheet answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
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