Math 270

Fall 2011

 

Test Prep Tips

Test-taking Tips

 

Summation Notation Sample Proof

Linear Combination of Matrices

Reah Explains How to Express AB as a Linear Combination of the Columns of A (He did it the long way!)

Hopefully somebody can explain it the short way.

Matrix Methods for Solving Linear Systems

Elementary Row Operations

Gaussian Elimination

Gauss-Jordan Reduction

Pivoting Method

Example of Pivoting

Todd Explains Pivoting

Peter Explains Trace

Laura Explains How to Find the Inverse of a Matrix

Dr. Sutcliffe Explains How to Find an Equivalent Matrix as Described in Section 2.4

Dr. Sutcliffe Explains Again How to Find an Equivalent Matrix as Described in Section 2.4

Hopefully someone can explain how to find the matrices P and Q for Dr. Sutcliffe’s example

Jesus Explains A=S+K

Nonsingular Product Implies Matrices are Singular

A and B row equivalent implies B=PA

 

Definition of a Real Vector Space

Examples of Real Vector Spaces

How to Show that a Given Set with Given Two Operations is NOT a Vector Space

Mimi Explains #12 Section 4.2

Real Vector Spaces Summary

Subspaces

How to Generate Subspaces

Laura Explains #18 Section 4.3

Peter Explains #25 Section 4.3

The Span of a Set

Spanning Set for a Vector Space

Natural Spanning Sets for Vector Spaces

Natural Spanning Sets for Subspaces

Minimal Spanning Sets

Linear Independence

Basis for a Vector Space

How to Find a Basis Given a Spanning Set

How to Find a Basis That Includes a Given Set of Vectors

Class was cancelled due to paint fumes so…

Coordinate Vector

Definition of Isomorphism

One-to-one and Onto Mappings

Isomorphism of n-dim Vector Spaces with

Isomorphic Vector Spaces

Transition Matrices

Example of Transition Matrices

Rank of a Matrix I

Rank of a Matrix II

Rank of a Matrix III

Jay Explains AX=0

Chapter 4 Review Part 1

Chapter 4 Review Part 2

Chapter 4 Review Part 3

Chapter 4 Review Part 4

 

Definition of Inner Product

Kari Explains How to Prove that An Operation is an Inner Product

The Matrix of an Inner Product

Example of a Matrix of an Inner Product

Evaluating an Inner Product Using the Standard Inner Product

The Matrix of an Inner Product is Positive Definite

Cauchy-Schwarz-Bunyakovsky Inequality

Finding the Inner Product Given the Matrix of the Inner Product

Angle Between Two Vectors

Triangle Inequality

Orthogonal Sets

Orthonormal Basis

Gram-Schmidt Process for Finding an Orthonormal Basis

Examples of the Gram-Schmidt Process

The Three Advantages of Using an Orthonormal Basis

Orthogonal Complements

Direct Sums of Subspaces

The Four Fundamental Subspaces of a Matrix

Linear Transformations Part 1

Linear Transformations Part 2

Linear Transformations Part 3

The Kernel of a Linear Transformation

The Range of a Linear Transformation

The Dimensions of the Domain, Kernel, and Range of a Linear Transformation

Invertible Linear Transformations

Finding the Inverse of a Linear Transformation

Linear Transformations Preserve Linear Independence

Kari Explains a Problem Involving a Linear Transformation and an Inner Product

37 Things to Know for Exam 3 # 1 – 8

37 Things to Know for Exam 3 # 9 – 13

37 Things to Know for Exam 3 # 14 – 15

37 Things to Know for Exam 3 # 9, 14, 15

37 Things to Know for Exam 3 # 16

37 Things to Know for Exam 3 # 17 – 33

37 Things to Know for Exam 3 # 34 – 35

37 Things to Know for Exam 3 # 36

37 Things to Know for Exam 3 # 36 – 37

Matrix of a Linear Transformation Part 1

Matrix of a Linear Transformation Part 2

Eigenvalues and Eigenvectors

Diagonalizable Linear Transformations

 

 

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