296CHAPTER19 The Matrix Morphing Game
There’s a neat way to solve three-by-three linear systems by removing the variables from the
notation. Only the coefficients remain, and these can be arranged into columns and rows to
form a table-like array called a matrix. In this chapter, you’ll learn how to manipulate matrixes
(ormatrices) to solve three-by-three linear systems.How to Build a Matrix
When you encounter a three-by-three linear system, each variable is multiplied by a constant
in each equation. Constants can also appear by themselves without variables. The form can
vary from one equation to another. Matrices aren’t so flexible. They have to be written in a
specific, standard form. Everything must go into a preassigned “cubbyhole.”The equation form
Before we can write any three-by-three linear system as a matrix, we have to get the triplet of
equations into the following form:a 1 x+b 1 y+c 1 z=d 1
a 2 x+b 2 y+c 2 z=d 2
a 3 x+b 3 y+c 3 z=d 3Where x,y, and z are the variables, and the letters a,b,c, and d with numeric subscripts
are the coefficients. A coefficient can be any real number including 0. When we want to
get a system into matrix form, we must write all the coefficients, even the ones that are
equal to 0!Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.