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Q10E

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Linear Algebra and its Applications
Found in: Page 191
Linear Algebra and its Applications

Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384

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Short Answer

If the null space of A \({\bf{7}} \times {\bf{6}}\) matrix A is 4-dimensional, what is the dimension of the column space of A?

The dimension of the column space of A is 1.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Find the rank of the matrix

Using the nullity theorem, you get:

\(\begin{aligned} {\rm{rank}}\,A &= n - \dim \,{\rm{Nul}}\,A\\ &= 6 - 5\\ &= 1\end{aligned}\)

Step 2: Find the dimension of the column space

The dimension of the column space of A is equal to its rank.

So, the dimension of the column space of A is 1.

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