Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.1 Exercises: 5

Answer

Replace row 2 with the sum of it and 3 times row 3, then replace row 1 with the the sum of it and -5 times row 3.

Work Step by Step

When we want to solve a system of linear equations in an augmented matrix, we want to first put it in a triangular form(which is a term to be replaced in the next section). Then we want to use the leading(from the left) 1 in each row to eliminate the entries within the same column. The matrix given to us is 1 -4 5 0 7 0 1 -3 0 6 0 0 1 0 2 0 0 0 1 -5 Since it is already in triangular form, and has already cleared out all but 1 entry on the first row from the right, we must clear out all but 1 entry from the 2nd row from the right. In order for us to do so, we must add 3 times the 3rd row to the 2nd row, and subtract 5 times the 3rd row from the 1st row. These two operations give us a new matrix: 1 -4 0 0 -3 0 1 0 0 12 0 0 1 0 2 0 0 0 1 -5 Which is closer to the solved stated of an augmented matrix.
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