Linear Algebra › Section C · Determinants › Topic C.3
Cramer's rule, volume, and transformations
Determinants give a formula for the solution of a square system, a formula for the inverse, and a precise meaning in geometry: they measure how a matrix scales area and volume and whether it flips orientation.
In this topic
- From a test to formulas and geometry
- Cramer's rule
- Worked example: Cramer's rule for two unknowns
- Why Cramer's rule works
- A formula for the inverse
- Determinants as area and volume
- Worked example: a triangle and a box
- How a transformation scales regions
- Orientation and where determinants reappear
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…