In this lesson, we learn about solving systems of linear equations using elimination with matrices. The method of elimination is a natural idea that is used in every software package to solve equations, and it is a straightforward way to get an answer in an efficient manner. We see how elimination works on a system of equations and how it decides whether the matrix is a good one or has problems. The lecture also discusses back substitution and expresses the operations of elimination in matrix language, which is how all the key ideas get expressed as matrix operations, not as words.
Elimination with Matrices -- Lecture #2. How to solve systems of linear equations by using elimination with matrices.
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
How do you use elimination to solve matrix Algebra problems?
How do you solve a system of 3 or more equations with elimination?
How is elimination used in Linear Algebra?
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This video is a very clear and thorough explanation of how to solve a system of linear equations manually by using elimination with matrices. Make sure you watch this video if you want to understand how to solve a matrix equation.