Unit 12: Cramer's rule, explained geometrically
About this unit
To solve Ax = v, replace a column of A with v and divide its determinant by det A: the signed area on the unknown input and a basis vector is scaled by det A, so each coordinate is a ratio of areas.
By the end, you can: Solve a 2×2 system with determinants and explain, with areas, why each unknown is a ratio of two determinants.
Modules
5 modulesLearn
- Areas that solve equationsArticle · Why each unknown of a 2×2 system is a ratio of two determinants: a signed area built from the unknown input is scaled by det A.Not started
- Solving a system with Cramer's ruleWalkthrough · Replace one column of A with the right-hand side, take determinants, divide by det A.Not started
- Negative determinants, and when it breaksWalkthrough · The signs take care of themselves when det A is negative; when det A is 0 the rule has nothing to divide by.Not started
- Cramer's rule in one pageReview · The rule, the reason behind it, when it applies and when to use something else.Not started