Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.8 Row Space and Column Space - Problems - Page 325: 3

Answer

a) The basis for row-space is of $A$ equal to $\{(1,2,3,4,5)\}$. b) The basis for column-space of $A$ is equal to $\{(1)\}$ with $m=1$.

Work Step by Step

a) We notice that there is only one row vector which is equivalent to basis of row space of $A$ with $n=5$. So, the basis for row-space is of $A$ equal to $\{(1,2,3,4,5)\}$. b) We notice that all column entries of $A$ are dependent $\{(1,2,3,4,5)\}$ . So, the basis for column-space of $A$ is equal to $\{(1)\}$ with $m=1$.
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