Math 392 Lecture 20 - Solving a system of linear equations with elementary row operations

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Welcome to lecture 20 of Linear Algebra and Vector Calculus!

In this lecture, we forge ahead with the linear algebra section of our course. Now that we know most of the basic definitions involving matrices, it's time for us to apply matrices to solving problems. It is noted that there are many applications of linear algebra (I forgot to mention a few I thought about), in particular, matrix theory--but the application most important to us is using matrices to solve linear systems of equations (several linear equations that may have the same solution).

We talk about how to write linear systems in terms of matrix equations and augmented matrices and then solve a couple simple systems using these matrix forms. We employ elementary row operations in order to get our matrices is convenient forms where the solution becomes evident. The process to do this is called row reduction or Gauss-Jordan elimination, the convenient forms are row echelon form and reduced row echelon form. All of these are defined and we play around with the concepts for a while to make sure we understand.
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Hello Mr. Smith, I was wondering, when you solved the example that started at 52:25, you got x=3, y=4. But, if you plugg x=3 and y=4 in the given equations x+2y=7 and 3x-y=7 it doesn't work. Can you please explain why? And is it possible to have different answers for x and y and still be correct? Thanks!

brianzar