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**Unformatted text preview: **m the constants on the right hand side, we use a vertical bar, |.
Note that in E 2, since y is not present, we record its coeﬃcient as 0. The matrix associated with
this system is
y
z c
x
(E 1) →
2
3 −1 1
(E 2) → 10
0 −1 2 (E 3) →
4 −9
25 8.2 Systems of Linear Equations: Augmented Matrices 467 This matrix is called an augmented matrix because the column containing the constants is
appended to the matrix containing the coeﬃcients.1 To solve this system, we can use the same
kind operations on the rows of the matrix that we performed on the equations of the system. More
speciﬁcally, we have the following analog of Theorem 8.1 below.
Theorem 8.2. Row Operations: Given an augmented matrix for a system of linear equations,
the following row operations produce an augmented matrix which corresponds to an equivalent
system of linear equations.
• Interchange any two rows.
• Replace a row with a nonzero multiple of itself.a
• Replace a row with itself plus a nonzero multiple of another row.b
a
b That is, the row obtained by multiplying...

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