INTRODUCTION TO MATRIX ALGEBRA

Transforming Matrix Algebra for the STEM Undergraduate

 

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ADEQUACY OF SOLUTIONS

CHAPTER 09

PRE-REQUISITES & OBJECTIVES

 

Pre-Requisites for Adequacy of Solutions [PDF] [DOC]

Objectives of Adequacy of Solutions [PDF] [DOC]

TEXTBOOK CHAPTER

 

Textbook Chapter of Adequacy of Solutions [PDF] [DOC]

DIGITAL AUDIOVISUAL LECTURES

 

ill-conditioned and well-conditioned system of equations [YOUTUBE 10:12] [TRANSCRIPT]

 

Row sum norm of a matrix Theory  [YOUTUBE 2:34]  [TRANSCRIPT]

Row sum norm of a matrix Example  [YOUTUBE 3:06]  [TRANSCRIPT]

 

How is the norm related to the conditioning of a system of equations Part 1 of 2  [YOUTUBE 8:55] [TRANSCRIPT]

How is the norm related to the conditioning of a system of equations Part 2 of 2 [YOUTUBE 5:58] [TRANSCRIPT]

Properties of norms [YOUTUBE 3:37] [TRANSCRIPT]

 

Relating changes in coefficient matrix to changes in solution vector [YOUTUBE 4:18]  [TRANSCRIPT]

Relating changes in coefficient matrix to changes in solution vector Proof [YOUTUBE 8:46]  [TRANSCRIPT]

Relating changes in right hand side vector to changes in solution vector  [YOUTUBE 3:12] [TRANSCRIPT]

 

Number of significant digits correct in my solution vector Theory [YOUTUBE 4:00]  [TRANSCRIPT]
Number of significant digits correct in my solution vector Example 1  [YOUTUBE 3:57]  [TRANSCRIPT]

Number of significant digits correct in my solution vector Example 2 [YOUTUBE 4:26]  [TRANSCRIPT]

 

PRESENTATIONS

 

Power Point Presentation on Adequacy of Solutions [PDF] [PPT]

MULTIPLE CHOICE TEST

 

Test Your Knowledge of Adequacy of Solutions  [FLASH] [PDF] [DOC] [SOLUTION]

PROBLEM SET
  Problem set for Adequacy of Solutions [PDF]  [DOC]

RELATED TOPICS

 

Introduction

Vectors

Binary Operations

Unary Operations

System of Equations

Gaussian Elimination

Gauss-Seidel Method

LU Decomposition

Adequacy of Solutions

Eigenvalues and Eigenvectors


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This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions orCreative Commons License recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Based on a work at http://mathforcollege.com/ma.  Introduction to Matrix Algebra is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.