**Math 270**

**Fall 2011**

**Summation
Notation Sample Proof**

**Linear
Combination of Matrices**

**Hopefully somebody can explain it the short way.**

**Matrix Methods
for Solving Linear Systems**

**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**

**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**

**Laura Explains
#18 Section 4.3**

**Peter Explains
#25 Section 4.3**

**Spanning Set
for a Vector Space**

**Natural
Spanning Sets for Vector Spaces**

**Natural
Spanning Sets for Subspaces**

**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…**

**Isomorphism of
n-dim Vector Spaces with **

**Example of
Transition Matrices**

**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**

**Gram-Schmidt Process for Finding an Orthonormal Basis**

**Examples of the Gram-Schmidt Process**

**The Three Advantages of Using an Orthonormal Basis**

**The Four Fundamental Subspaces of a Matrix**

**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**

**Diagonalizable Linear Transformations**

** **