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.
6 reference pages
Operations on matrices: addition, scalar multiplication and matrix multiplication with worked 3×3 and 2×2 examples, why AB ≠ BA, the transpose of a product, and common mistakes.
Special types of matrices: diagonal, scalar, identity, zero and triangular matrices, how they multiply and their determinants, finding missing entries, worked examples and common mistakes.
Symmetric and skew-symmetric matrices: definitions, splitting any square matrix into both, a 2×2 and a 3×3 worked example, key properties including the zero determinant of odd-order skew matrices, and common mistakes.
What a square matrix is, how to square a matrix, determinant properties including |kA| and |adj A|, idempotent matrices, singular systems, and common mistakes.
Solving a system of linear equations using matrices: the matrix method X = A⁻¹B with the adjoint, worked 2×2 and 3×3 examples, the consistency test, and common mistakes.
The area of a triangle from its vertices using a determinant, with worked examples, a collinearity test, finding an unknown vertex from a given area, and common mistakes.