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).
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
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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