Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 8 - Systems of Linear Equations and Problem Solving - 8.7 Determinants and Cramer's Rule - 8.7 Exercise Set - Page 557: 33


The answer is below.

Work Step by Step

If these two equations are dependent, this means that they are the same equation, but one is multiplied by some constant $k$. Thus, when we find the determinant of the matrix, we will find: $$a_1b_2-b_1a_2$$ However, since the two equations are dependent, $a_1b_2\ and\ b_1a_2$ will be equal, so the expression above will evaluate to zero.
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