Algebra › Section D · Systems of linear equations › Topic D.7
Solving systems with determinants
Elimination is a process; Cramer's rule is a formula. Package the coefficients into a grid, turn the grid into a single number called a determinant, and the solution to a system falls out of division.
In this topic
- From grid to single number
- The 2×2 determinant
- Cramer's rule for two variables
- Worked example: a 2×2 system by Cramer's rule
- Minors: shrinking a 3×3 to three 2×2s
- Worked example: a 3×3 determinant
- Cramer's rule for three variables
- When D = 0, the rule goes quiet
- Collinearity: a determinant as a geometry test
- Common mistakes to avoid
- Key takeaways
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