Lecture 3: Matrices and Inverse Matrices
In this lesson, you'll learn about matrices and how to find inverse matrices as they relate to vectors. The lesson covers the basics of matrix multiplication and provides examples of how to apply it to solve problems, such as finding the equation of a plane in space. The lesson also touches on the cross product of vectors and its geometric definition. By the end of the lesson, you'll have a solid understanding of the fundamentals of matrices and their applications.
Learn how to use matrices and find inverse matrices as they pertain to vectors.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
- Problem Set - A problem set with some problems from this lecture.
- How do you write a matrix from vectors?
- How do you find the determinant of a vector matrix?
- Why is A x B the opposite of B x A?
- Why does A x A = 0?
- Why is the cross product of a vector with itself equal to 0?
- How do you find the equation of a plane that contains three points in space?
- How do you find a normal vector that is perpendicular to a plane?
- What is a triple product?
- How do you multiply matrices?
- How do you find the inverse of a matrix?
- What is the identity matrix?
- When can two matrices be multiplied?
- What is the formula to find an inverse matrix?
- What is an adjoint matrix?
- How do you find the determinant of a matrix using minors?
- What are cofactors of a matrix?
- What is the transpose of a matrix?
- How do you write a matrix from vectors?
- How do you find the determinant of a vector matrix?
- Why is A x B the opposite of B x A?
- Why does A x A = 0?
- Why is the cross product of a vector with itself equal to 0?
- How do you find the equation of a plane that contains three points in space?
- How do you find a normal vector that is perpendicular to a plane?
- What is a triple product?
- How do you multiply matrices?
- How do you find the inverse of a matrix?
- What is the identity matrix?
- When can two matrices be multiplied?
- What is the formula to find an inverse matrix?
- What is an adjoint matrix?
- How do you find the determinant of a matrix using minors?
- What are cofactors of a matrix?
- What is the transpose of a matrix?
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Staff Review
This lesson is crucial to understanding vectors in this course. Several applications of vectors are discussed, such as finding the equation of a plane that contains three points in space. You will also learn to write a vector matrix, find the determinant, and find inverse matrices. If you have not had a Linear Algebra course, this is a vital lecture. It is a nice refresher either way, however. -
