Unformatted text preview: pounds of Type I,
3 − 1 t pounds of Type II and t pounds of Type III where 0 ≤ t ≤ 4 .
3 466 8.2 Systems of Equations and Matrices Systems of Linear Equations: Augmented Matrices In Section 8.1 we introduced Gaussian Elimination as a means of transforming a system of linear
equations into triangular form with the ultimate goal of producing an equivalent system of linear
equations which is easier to solve. If take a step back and study the process, we see that all of our
moves are determined entirely by the coeﬃcients of the variables involved, and not the variables
themselves. Much the same thing happened when we studied long division in Section 3.2. Just as
we developed synthetic division to streamline that process, in this section, we introduce a similar
bookkeeping device to help us solve systems of linear equations. To that end, we deﬁne a matrix
as a rectangular array of real numbers. We typically enclose matrices with square brackets, ‘[ ’ and
‘ ]’, and we size matrices by the number of rows and columns they have. For example, the size
(sometimes called the dimension) of
2 −5 10
is 2 × 3 because it has 2 rows and 3 columns. The individual numbers...
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