How do we represent a system of linear equations using matrices? This is a handy skill to have, which we will use constantly as we continue to study matrices, and we go over it in detail in today's full linear algebra video lesson.

First we show how to represent a system of linear equations using 3 matrices. These three matrices are the coefficient matrix, the variable matrix, and the constant matrix. Then, using an augmented matrix, we represent the whole system of linear equations using just one matrix!

Representing a system of linear equations using one matrix is useful because it allows us to solve a system of linear equations using matrices. We perform what are called row operations on the matrix, and if we do it just right, which we will go over in another lesson, we can get the matrix into what is called reduced row echelon form, which gives us the solution to the system!


I hope you find this video helpful, and be sure to ask any questions down in the comments!

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