Linear systems in two unknowns are solved by substitution, reduction or Cramer. With unknowns the theory changes little, but the notation changes a lot: it is convenient to pack the coefficients into a matrix. What follows is a minimal capsule (beyond the standard Year 5 syllabus), useful as a springboard for physics and computer science: operational definitions on matrices, addition and product, the inverse matrix, writing a system in matrix form and Gaussian elimination.
- Matrices, operational definitions
- Addition of matrices and product by a scalar
- Row-by-column product
- Example, product of two matrices
- Inverse of a 2x2 matrix
- Linear systems in matrix form
- Gaussian elimination method
- Example, 3x3 system with Gauss
- Comparison between Gauss and Cramer
- Degenerate cases of Gauss