Download linear-algebra-11-curriculum

Linear Algebra 11
Course Material and time required
Topic
Days expected
Unit 1: Prep and Review
1 day
Equations of Lines
Graphing Lines
Algebra, Linear Equations
Systems of equations
4 days
Additional notes
First week is intended to be a
review week. To get students up
to where I want them to be for
the main course work. Section
2.1 in the textbook.
Unit 2: Vectors
2
3
Vectors in R and R
Vector notation
2 Days
Vector equation of a line
Other Definitions
Vectors in Rn
Vector Spaces
3 Days
Subspaces
Span and Linear Independence
Standard Basis
Length and Dot Product
In R2 and R3
2 Days
Definitions: Dot product, norm,
Triangle Inequality, Unit
Vectors
Projection and Minimum Distance
Projections
1 Day
Minimum Distance
1 Day
Cross Product and Volumes
Cross Product Definition
1 Day
Length of the cross product
Volume
Unit 3: Introduction to Matrices
The Matrix Representation of a System
Matrix Representation
1 Day
Row operations
Row echelon form
1 Day
Which systems have solutions?
1 Day
Short cuts and bad ideas
Reduced Row Echelon Form
Definition
Do we even Care?
Rank
1 Day
Homogeneous Solutions
Infinite solutions
Section 1.1
Section 1.2
Section 1.3
Give a day of work in here for
students to play around with all
those definitions introduced.
Section 1.4
Section 1.5
Work days should go in here. At
least 2.
Rest of section 2.1
Lots of examples
Example 12 in the Text
Section 2.2
Applications
Span of Vectors
Linear Independence
Bases of Subspaces
1 Day
1 Day
1 Day
Applications of Systems
Linear Programming
1 Day
Unit 4: Matrices 2
Matrix Operations
Equality, Addition, Scalar
1 Day
Multiplication
Transpose
Matrix Multiplication
2 Days
Summation Notation
Multiplication Facts
Identity Matrix
Matrix Mapping and Linear Maps
Matrices are functions for
Vectors!
1 Day
Properties
Specifics: Linear mappings
1 Day
Linear Map = Matrix Map?
Composition of Maps
1 Day
Geometric Maps
Rotations
1 Day
Rank Theorem
Solution Space
Null Space
Solution Set of Ax = b
Section 2.3
These sections are JUST long
enough to introduce and then
do some examples. Add some
time to practice all of section 2
in this space.
Section 2.4
Section 3.1
Keep referencing back to
normal Multiplication of
numbers. (How multiplication is
usually commutative, has a
cancellation law, etc.)
Section 3.2
Properties are the natural
extension of normal functions
Section 3.3
Short – For interest and time to
give work time to students
Section 3.4
1 Day
Range of L and Column Space of A
1 Day
Rowspace
2 Days
Bases of Row/ColumnSpace
Rank-Nullity Theorem
Inverse Matrices
What is that?
1 Day
Procedure
Some Facts: Summary
Unit 5: Vector Spaces
Spaces of Polynomials
Polynomial addition
subtraction
<1 Day
Properties (Familiar?)
Examples
Vector Spaces
Abstract Definition
End of Day with Sec. 4.1
Section 3.5
Section 4.1
Section 4.2
Examples of Vector Spaces
1 Day
Subspaces
Bases and Dimensions
Section 4.3
Definitions
1 Day
Obtaining a basis from a
spanning set of vectors
All bases have the same
dimension
1 Day
How to make a basis out of a LI
set
Theorem 4 and conclusion
Unit 6: Determinants
Finding Inverses
Section 5.1
In terms of cofactors
1 Day
3x3 case
1 Day
Solo work time in here
General Case
Row Operations
Section 5.2
How Row operations change
1 Day
the determinant
Related to Invertibility
1 Day
Product of matrices
Matrix inverse by Cofactors
Section 5.3
Definition of a cofactor matrix
1 Day
A-1 in terms of cofactors
Area, Volume, Determinant
Section 5.4
How are area and determinant
related?
1 Day
Determinant and volume
Unit 7: Eigenvalues and Eigenvectors, Diagonalization
Eigenvalues and eigenvectors
Section 6.1
What even are those?
1 Day
Of a mapping? Of a matrix?
Procedure to find them
At least 2 days
Lots of practice
Diagonalization
Section 6.2
Related to Eigenvalues/vectors
D = PAP-1, how to find
THE END!