# determinant and volume

(1.1 hours to learn)

## Summary

The volume of a box in n dimensions is given by the determinant of the matrix whose columns are the sides of the box. When a matrix is used as a linear transformation, it scales the volume of a set by its determinant.

## Context

This concept has the prerequisites:

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

## -Free-

→ Khan Academy: Linear Algebra

- Lecture "Determinant and area of a parallelogram"
- Lecture "Determinant as scaling factor"

→ MIT Open Courseware: Linear Algebra (2011)

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

## -Paid-

→ 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," subsection "Area of a triangle," pages 271-274

## See also

-No Additional Notes-