Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 22: 29


This system is inconsistent - it has not solutions.

Work Step by Step

Follow the steps below Step 1: Add to the third equation the first one multiplied by $4/3$ to eliminate $x$: $$4x+\frac{4}{3}(-3x)-8y+\frac{4}{3}5y = 32 +\frac{4}{3}(-22)$$ which becomes $$-8y+\frac{20}{3}y = 32-\frac{88}{3}\Rightarrow -\frac{4}{3}y = \frac{8}{3}$$ and this gives $$y=-2.$$ Step 2: Add the 1st equation to the second to eliminate $x$: $$3x-3x+4y-5y=4-22$$ which gives $$y= 18.$$ Now note that this is in contradiction with what we got in the step one since $y$ cannot be both $-2$ and $18$ so this system is inconsistent and has no solutions.
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