Class 12 matrices and determinants: the special types of matrices, matrix operations, symmetric and skew-symmetric matrices, determinants and their properties, and solving systems of linear equations with matrices.
7 reference pages
How matrix addition and multiplication work, with a worked multiplication example.
Diagonal, scalar, and identity matrices explained, with examples showing how each one is a more specific case of the last.
What symmetric and skew-symmetric matrices are, and how to split any square matrix into a sum of both, with a worked example.
Key facts about square matrices: the determinant scaling rule, idempotent matrices, and when a matrix equation has no solution.
How to solve a system of linear equations using the matrix method, with a fully worked three-variable example.
Solving for unknown entries in a matrix using a stated property or a matching determinant, with worked examples.
The determinant formula for the area of a triangle from its vertex coordinates, with a worked example.