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The four subspaces that stays same when the first two rows of A are exchanged. Also, to write down the
Yes, the four subspaces and row space stay the same when first two rows of matrix A are exchanged.
The vector in left subspace of the new matrix is:
Given:
Left nullspace of A is
Calculation:
Even after the rows of a matrix are exchanged, rows stay themselves and the subspaces whose bases are already pre-determined also stay the same. Therefore, the four subspaces and row space stay the same when first two rows of matrix A are exchanged.
Switch rows of the matrix means the order of the equation is changed, however, the result remains the same as that of old matrix. Thus, if
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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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