Chapter 10
APPLICATIONS OF MATRIX ALGEBRA
Chapter 9 introduced matrices, explored matrix operations, and culmi-
nated with Cramer’s Rule, a method by which to solve systems of linear
equations using matrices. This chapter is organized in a similar fashion. It
begins with the manipulation of matrices, specifically row operations and
row echelon form, and evolves into a set of matrix applications, including a
method by which to solve nontrivial systems of equations. The chapter also
explores inverse matrices, which are necessary to solve matrix equations.
In this chapter, you learn how to put matrices in row echelon form
and reduced-row echelon form. It’s sort of like putting linear equations
into standard form, but with greater benets. The biggest benet?
When you put an augmented matrix in reduced-row echelon form, you’ve
automatically solved the corresponding system of equations! Before
that, however, you need to master row operations—things you’re allowed
to do to a matrix to get it in the right form.
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