Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - Supplementary Exercises - Page 90: 10

Answer

Has unique solution

Work Step by Step

As you can see from graph, vectors $a_{1}$ and $a_{2}$ are linearly independent. Since they are linearly independent, matrix $\left[\begin{array}{ll}a_{1} & a_{2}\end{array}\right]$ has both pivot columns. This means that every vector in $\mathbb{R}^{2}$ can be written as a linear combination of $a_{1}, a_{2}$ In other words, $A x=b$ has unique solution for every $b$
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