Let A = 113 -1 0-1 214 (a) Find a basis for Row A. (b) Find a basis for Nul A. (c) Verify Theorem 5.1 from the notes. Note: for parts where a basis is asked for it is essential to unambigu- ously state what the basis is, ideally finishing with "a basis for Row A is..." rather than "RowA=...". You must be precise in use of mathematical terminology.
Let A = 113 -1 0-1 214 (a) Find a basis for Row A. (b) Find a basis for Nul A. (c) Verify Theorem 5.1 from the notes. Note: for parts where a basis is asked for it is essential to unambigu- ously state what the basis is, ideally finishing with "a basis for Row A is..." rather than "RowA=...". You must be precise in use of mathematical terminology.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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attached is the question and therom 5.1
![Theorem 5.1. If A is an m x n matrix then
dim Nul A + dim Row A = n.
Returning to our original motivation for studying this shows that as we
increase the size (dimension!) of the space of equations in our linear system
Ax = 0 (dim Row A) we decrease the size (dimension!) of the space of solutions
(dim Nul A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ac09755-9639-4075-b6f1-d2ae73f82d81%2Ff38f4a1e-52d3-46c3-89a8-89f93d9c1637%2Fgk2tnwg_processed.png&w=3840&q=75)
Transcribed Image Text:Theorem 5.1. If A is an m x n matrix then
dim Nul A + dim Row A = n.
Returning to our original motivation for studying this shows that as we
increase the size (dimension!) of the space of equations in our linear system
Ax = 0 (dim Row A) we decrease the size (dimension!) of the space of solutions
(dim Nul A).
![Let
A =
11 3
-1 0-1
21 4
(a) Find a basis for Row A.
(b) Find a basis for Nul A.
(c) Verify Theorem 5.1 from the notes.
Note: for parts where a basis is asked for it is essential to unambigu-
ously state what the basis is, ideally finishing with "a basis for Row
A is..." rather than "RowA = ...". You must be precise in use of
mathematical terminology.
Fil](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ac09755-9639-4075-b6f1-d2ae73f82d81%2Ff38f4a1e-52d3-46c3-89a8-89f93d9c1637%2Fw72jn8_processed.png&w=3840&q=75)
Transcribed Image Text:Let
A =
11 3
-1 0-1
21 4
(a) Find a basis for Row A.
(b) Find a basis for Nul A.
(c) Verify Theorem 5.1 from the notes.
Note: for parts where a basis is asked for it is essential to unambigu-
ously state what the basis is, ideally finishing with "a basis for Row
A is..." rather than "RowA = ...". You must be precise in use of
mathematical terminology.
Fil
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