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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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