Cramer's Rule, Inverse Matrix, and Volume
In this lesson, we learn about Cramer's Rule, Inverse Matrix, and Volume. The lecture focuses on finding formulas for determinants and using them to calculate the inverse of a matrix. The formula for the inverse is obtained by dividing the matrix of cofactors by the determinant. The lecture also discusses how to use the inverse to solve linear systems, and Cramer's rule is introduced as a way to find the solutions of a linear system by using determinants.
Cramer's Rule, Inverse Matrix, and Volume -- Lecture 20. Using Cramer's Rule, determinants and finding inverses and the volume of a box with matrices.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- What is Cramer's Rule?
- How do you find the inverse of a matrix?
- How do you find volume of a box with a matrix?
- What is a formula for A inverse?
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Staff Review
The final lecture on determinants. Finally, determinants are used in an application of finding the volume of a box with determinants. Cramerâs Rule is introduced, and inverses and determinants are used in applications of real-world problems.
