# Cramer's rule

(35 minutes to learn)

## Summary

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.

## Context

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.)

## Goals

- Be able to use Cramer's rule to solve linear systems and compute matrix inverses

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ 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

## See also

-No Additional Notes-