- 1. Meet the Matrix: Naming Its Rows, Columns, and Elements
State what a matrix is, identify its rows, columns and elements, and use double-subscript notation a_ij to name and locate any element by its row and column.
- 2. The Order of a Matrix
State the order of a matrix as rows by columns, recognise row, column and 1 by 1 matrices, and use the order to count a matrix's elements.
- 3. Equal Matrices
State the two conditions for two matrices to be equal, and use matrix equality to form equations and solve for unknown elements.
- 4. Special Types of Matrices
Identify a square matrix and recognise the diagonal, identity (unit) and null (zero) matrices on sight.
- 5. Adding and Subtracting Matrices
Apply the same-order rule for matrix addition and subtraction, combine corresponding elements, and recognise that addition is commutative but subtraction is not.
- 6. Scalar Multiplication and Linear Combinations
Multiply a matrix by a scalar, combine scalar multiplication with addition and subtraction, and solve for an unknown matrix.
- 7. Multiplying Two Matrices
State the compatibility condition for matrix multiplication, compute products by pairing rows with columns, and recognise that matrix multiplication is not commutative.
- 8. The Inverse of a 2x2 Matrix
State that A times its inverse gives the identity and exists only when the determinant is non-zero, and find a 2x2 inverse using swap-negate-divide.
- 9. Solving Simultaneous Equations with Matrices
Write a pair of linear equations as a matrix equation AX = B, solve by the inverse-matrix method, and solve by Cramer's rule.
