Linear Algebra and Its Applications (5th Edition)

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

Chapter 4 - Vector Spaces - 4.6 Exercises - Page 239: 11

Answer

$dim\,row A=3$

Work Step by Step

Given the null space of a 8 x 5 matrix, A, is 2-dimensional; We are required to find the dimension of the row space of A $Rank=n-dim\,Nul A$ $n=5$ and $dim\,Nul A=2$ therefore; $Rank A=5-2=3$ the rank of a matrix is equal to the number of pivot rows. the number of pivot rows is equal to the dimension of the row space of A=3. the dimension of the row space of $A=3$
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