(35 minutes to learn)
Cramer's rule is an explicit formula for the inverse of a matrix in terms of determinants of submatrices. While it is inefficient for large matrices, it is useful for analyzing inverses of small matrices algebraically.
This concept has the prerequisites:
- linear systems as matrices (Cramer's rule is an explicit solution to linear systems.)
- matrix inverse (Cramer's rule is an explicit formula for matrix inverses.)
- determinant (Cramer's rule involves determinants.)
- Be able to use Cramer's rule to solve linear systems and compute matrix inverses
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 7.5, "Determinants and n-dimensional volume," from pages 318-320
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 5.3, "Cramer's rule, inverses, and volumes," up to "Area of a triangle," pages 269-271
-No Additional Notes-
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation