Lessons in this chapter
- 1Understanding and Evaluating DeterminantsTurn a square array into a number and learn to evaluate determinants with a clear choice of row or column.
- 2Determinants and the Area of a TriangleUse one coordinate determinant to calculate area, recognise collinearity, and describe a line.
- 3Minors and CofactorsGive each deleted-row determinant a name and use signed cofactors to explain expansion and cancellation.
- 4Adjoints and Inverse MatricesBuild an adjoint from cofactors, establish when an inverse exists, and connect inverse calculations to matrix identities.
- 5Solving Systems with Matrix InversesRepresent equations as AX=B, test what their coefficient matrix tells you, and solve consistent systems with a unique solution.
- 6Chapter Summary and PracticeConnect determinant calculations, geometry, adjoints, inverses, and systems through complete mixed worked problems.