How can matrices be used when solving by substitution?

1 Answer
Apr 7, 2018

The process of "solving" a matrix and solving a system of equations are mathematically identical.

Suppose you have some system with #3# unknowns and #3# equations. Say,

#3x + 4y + 9z = 26#,
#5x - 2y + 3z = 13#,
#x + y - 2z = 10#.

This is equivalent to the matrix equation

#((2, 4, 9),(5, -2, 3),(1, 1, -2))*((x),(y),(z)) = ((26),(13),(10))#.

To solve this, one would set up an augmented matrix and use row-reduction techniques to find your solution. The bolded methods are outside the scope of basic algebra and you will run across them if you ever take a linear algebra course.

Just know that row-reduction techniques simulate substitution and that it is not (mathematically) easier to use a matrix to solve a system than to solve a system in the traditional way.