In this lesson, the teacher covers the rules for matrix multiplication and how to find inverse matrices. There are four ways to multiply matrices, including by columns, rows, and blocks, and each method produces the same answer. The teacher also explains that not all matrices have inverses, but if they do, the inverse can be on either the left or the right side of the matrix. For square matrices, a left inverse is also a right inverse if one exists.
Multiplication and Inverse Matrices -- Lecture #3. How to multiply matrices and find and use inverse matrices to solve systems of linear equations.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 17, 2008). License: Creative Commons BY-NC-SA. More info at: http://ocw.mit.edu/terms
Questions answered by this video:
How do you multiply matrices?
What is an inverse matrix?
How do you find an inverse matrix?
What is a nonsingular matrix?
What is a singular matrix?
Currently 4.0/5 Stars.
This video explains very well (though at times it can be difficult to follow) how to use inverse matrices to solve systems of equations, and why this works. Also, multiplying matrices is explained.