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Topic 5: Further matrices

Matrix algebra and systems of equations

5 hours

• Calculate the determinant and multiplicative inverse of square matrices of any order, with technology.
• Use the determinant to determine whether a square matrix of any order is singular or non-singular.
• Use matrix algebra to solve matrix equations that involve matrices of beyond dimension 2 × 2, including those of the form AX = B, XA = B and A + X = B, with technology.
• Model and solve problems that involve matrices of beyond dimension 2 × 2, including the solution of systems of linear equations, with technology.
• Recognise the general form of a system of linear equations in several variables and use Gaussian techniques of elimination on an augmented matrix to solve a system of linear equations, with and without technology. 1 interactive
• Examine the three cases for solutions of systems of equations — a unique solution, no solution and infinitely many solutions — and the geometric interpretation of a solution of a system of equations with three variables including a unique solution, no solution and infinitely many solutions. 1 interactive

Applications of matrices

7 hours

• Model and solve problems that involve real-life situations using matrices, including Dominance and Leslie matrices. 2 interactives
• Investigate how matrices have been applied in other real-life situations, e.g. Leontief, Markov, area, cryptology, eigenvectors and eigenvalues. Note: The external examination may assess only Dominance and Leslie matrices.