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 24: 52

Answer

Infinite number of solutions.

Work Step by Step

$Since\:the\:system\:has\:a\:unique\:solution,\:we\:know\:that\:none\:of\:the\:equations\:is\:a\:multiple\:of\:another\:and\:there\:are\:no\:inconsistencies\:in\:any\:of\:the\:equations.\:Therefore,\:when\:using\:only\:two\:of\:the\:three\:equations,\:we\:have\:more\:variables\:than\:equations.\:As\:a\:result,\:by\:Theorem\:1.1,\:this\:states\:that\:if\:there\:are\:more\:variables\:than\:equations,\:there\:will\:be\:an\:infinite\:number\:of\:solutions.$
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