(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:
- 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
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