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 - 1.2 Exercises: 27

Answer

The columns in the coefficient matrix are all pivot columns.

Work Step by Step

The reduced row echelon form of the augmented matrix is $\left[ \begin{array}{cccc} 1 & 0 & 0 &...&0&a_1\\ 0 & 1&0&...&0&a_2\\ \vdots & &\ddots & &0&\vdots \\ \vdots & & &\ddots \\ 0& ...&...&...&1&a_n \end{array} \right],$ where $a_1$,...,$a_n$ are numbers. We can see the last column (on the right) is not a pivot column and the corresponding system of equations will have no free variables. Hence the system is consistent and has a unique solution.
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