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Stitz-Zeager_College_Algebra_e-book

# To that end consider the system 2x 3y 16 3x 4 y 7 to

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Unformatted text preview: each entry in the row by the same nonzero number. Where we add entries in corresponding columns. As a demonstration of the moves in Theorem 8.2, we revisit some of the steps that were used in solving the systems of linear equations in Example 8.1.2 of Section 8.1. The reader is encouraged to perform the indicated operations on the rows of the augmented matrix to see that the machinations are identical to what is done to the coeﬃcients of the variables in the equations. We ﬁrst see a demonstration of switching two rows using the ﬁrst step of part 1 in Example 8.1.2. 3x − y + z = 3 x−y+z = 5 (E 1) (E 1) Switch E 1 and E 3 (E 2) 2x − 4y + 3z = 16 − − − − − − (E 2) 2x − 4y + 3z = 16 − − − − −→ (E 3) x−y+z = 5 (E 3) 3x − y + z = 3 3 −1 13 1 −1 15 Switch R1 and R3 2 −4 3 16 − − − − − − 3 16 − − − − − → 2 −4 1 −1 15 3 −1 13 Next, we have a demonstration of replacing a row with a nonzero multiple of itself using the ﬁrst step of part 3 in Example 8.1.2. (E 1) 3x1 + x2 + x4 = 6 (E...
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