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The bases for the four subspaces for A when the 3 by 3 matrix is invertible and also for the 3 by 6 matrix
For A,
Row space basis and column space basis is
For B,
Row space basis
Given:
Invertible 3 by 3 matrix A and 3 by 6 matrix
Calculation:
Consider the invertible 3 by 3 matrix A,
Row space basis
Nullspace basis and left nullspace basis both are empty because Z is empty.
Consider 3 by 6 matrix
Row space basis is
Column space basis is
Left nullspace basis is empty because Z is empty
Nullspace basis is
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Chapter 3 Solutions
Introduction to Linear Algebra, Fifth Edition
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
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