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Q7E

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Linear Algebra With Applications

Found in: Page 245

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Consider a symmetric $n \times m$ matrix A. What is the relationship between Im(A) and ker(A) ?

The relation between $im (A) and {(kerA)}^{⊥} is im (A) = {(kerA)}^{⊥}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Determine the relation.

Consider a $n \times m$ matrix A .

Theorem: For any matrix B , $im (B) = {(kerB)}^{⊥}$ .

By the theorem, im(A)= ${(k e r B)}^{⊥}$ .

Step 2: Draw the graph of relation between Im(A) and ker (A) .

Sketch the graph to show the relation between $i m (A) a n d {(k e r A)}^{⊥}$

Hence, the relation between $i m (A) a n d {(k e r A)}^{⊥} i s i m (A) = {(k e r A)}^{⊥}$ .

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