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<MIT Linear Algebra, Lecture 2: Elimination with Matrices ⁄ >

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This is the second post in an article series about MIT's course "Linear Algebra". In this post I will review lecture two on solving systems of linear equations by elimination and back-substitution. The other topics in the lecture are elimination matrices and permutation matrices.

The first post covered the geometry of linear equations.

One of my blog readers, Seyed M. Mottaghinejad, had also watched this course and sent me his lecture notes. They are awesome. Grab them here: lecture notes by Seyed M. Mottaghinejad (includes .pdf, .tex and his document class).

Okay, here is the second lecture.

Lecture 2: Elimination with Matrices

Elimination is the way every software package solves equations. If the elimination succeeds it gets the answer. If the matrix A in Ax=b is a "good" matrix (we'll see what a good matrix is later) then the elimination will work and we'll get the answer in an efficient way. It's also always good to ask how can it fail. We'll see in this lecture how elimination decides if the matrix A is good or bad. After the elimination there is a step called back-substitution to complete the answer.

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