Linear Algebra
SAT Score Range
•
25 sessions
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JS
MT
GW
+12
•
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About
I am back to host another wonderful series: LINEAR ALGEBRA! I hope you all can join!
This series will cover the content of a semester of college Linear Algebra and is traditionally taken after Calculus
PREREQ:
Pre-Calculus (Surprising, right?) . . . but I STRONGLY recommend a successful completion of AP® Calculus BC
why the Prereq?
You don't use Calculus in this course, but understanding vectors and matrices well will get you ahead. The only part in AP® Calculus BC useful for this is the vectors unit, so please review that on your own because we will do a quick recap of the basics of vectors and matrices when this series begins!
STRUCTURE:
1. Lecture (60-90 min)
2. Optional Homework
*repeat above until unit is complete*
3. Problem Set for the Unit
4. Unit TEST
Here is the syllabus for the series:
1. Matrices and Systems of Equations
2. Matrix Operations and Matrix Inverses
3. Determinants
4. Norm, Inner Product, and Vector Spaces
5. Basis, Dimension, and Subspaces
6. Linear Transformations
7. Eigenvalues and Eigenvectors
Tutored by
✋ ATTENDANCE POLICY
USE THE TUTOR CHAT to message me if you won't be here BEFORE the session starts (this counts as an excused absence!)
IF YOU EXCEED 3 CONSECUTIVE UNEXCUSED ABSENCES, you will, unfortunately, be removed from the series
SESSION 1
4
Feb
SESSION 1
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCFeb 4, 9:30 PM - 10:30 PM UTC
Matrices and Systems of Equations DAY 1
1. Use correct matrix terminology to describes various types and features of matrices (triangular, symmetric, row echelon form, et.al.)
2. Use Gauss-Jordan elimination to transform a matrix into reduced row echelon form
SESSION 2
5
Feb
SESSION 2
Other Topics
Other Topics
Wed 9:30 PM - 10:30 PM UTCFeb 5, 9:30 PM - 10:30 PM UTC
Matrices and Systems of Equations DAY 2
3. Determine conditions such that a given system of equations will have no solution, exactly one solution, or infinitely many solutions
4. Write the solution set for a system of linear equations by interpreting the reduced row echelon form of the augmented matrix, including expressing infinitely many solutions in terms of free parameters
SESSION 3
7
Feb
SESSION 3
Other Topics
Other Topics
Fri 9:30 PM - 10:30 PM UTCFeb 7, 9:30 PM - 10:30 PM UTC
Matrices and Systems of Equations DAY 3
5. Write and solve a system of equations modeling real-world situations such as electric circuits or traffic flow
SESSION 4
11
Feb
SESSION 4
Review
Review
Tue 9:30 PM - 10:15 PM UTCFeb 11, 9:30 PM - 10:15 PM UTC
This is intended as a Linear Algebra Review Session before our Assessment or in between topics
SESSION 5
14
Feb
SESSION 5
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCFeb 14, 9:30 PM - 11:00 PM UTC
Matrices and Systems of Equations TEST (02/14)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 6
18
Feb
SESSION 6
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCFeb 18, 9:30 PM - 10:30 PM UTC
Matrix Operations and Matrix Inverses DAY 1
1. Perform the operations of matrix-matrix addition, scalar-matrix multiplication, and matrix-matrix multiplication on real and complex-valued matrices
SESSION 7
21
Feb
SESSION 7
Other Topics
Other Topics
Fri 9:30 PM - 10:30 PM UTCFeb 21, 9:30 PM - 10:30 PM UTC
Matrix Operations and Matrix Inverses DAY 2
2. State and prove the algebraic properties of matrix operations
3. Find the transpose of a real-valued matrix and the conjugate transpose of a complex-valued matrix
SESSION 8
24
Feb
SESSION 8
Other Topics
Other Topics
Mon 9:30 PM - 10:30 PM UTCFeb 24, 9:30 PM - 10:30 PM UTC
Matrix Operations and Matrix Inverses DAY 3
4. Identify if a matrix is symmetric (real-valued)
5. Find the inverse of a matrix, if it exists, and know conditions for invertibility.
6. Use inverses to solve a linear system of equations
SESSION 9
25
Feb
SESSION 9
Review
Review
Tue 9:30 PM - 10:15 PM UTCFeb 25, 9:30 PM - 10:15 PM UTC
This is intended as a Linear Algebra Review Session before our Assessment or in between topics
SESSION 10
28
Feb
SESSION 10
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCFeb 28, 9:30 PM - 11:00 PM UTC
Matrix Operations and Matrix Inversess TEST (02/28)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 11
3
Mar
SESSION 11
Other Topics
Other Topics
Mon 9:30 PM - 10:30 PM UTCMar 3, 9:30 PM - 10:30 PM UTC
Determinants DAY 1
1. Compute the determinant of a square matrix using cofactor expansion
2. State, prove, and apply determinant properties, including determinant of a product, inverse, transpose, and diagonal matrix
SESSION 12
4
Mar
SESSION 12
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCMar 4, 9:30 PM - 10:30 PM UTC
Determinants DAY 2
3. Use the determinant to determine whether a matrix is singular or nonsingular
4. Use the determinant of a coefficient matrix to determine whether a system of equations has a unique solution
SESSION 13
7
Mar
SESSION 13
Review
Review
Fri 9:30 PM - 10:15 PM UTCMar 7, 9:30 PM - 10:15 PM UTC
This is intended as a Linear Algebra Review Session before our Assessment or in between topics
SESSION 14
10
Mar
SESSION 14
Other Topics
Other Topics
Mon 8:30 PM - 10:00 PM UTCMar 10, 8:30 PM - 10:00 PM UTC
Determinants TEST (03/10)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 15
11
Mar
SESSION 15
Other Topics
Other Topics
Tue 8:30 PM - 10:00 PM UTCMar 11, 8:30 PM - 10:00 PM UTC
Norm, Inner Product, and Vector Spaces DAY 1
1. Perform operations (addition, scalar multiplication, dot product) on vectors in Rn and interpret in terms of the underlying geometry
2. Determine whether a given set with defined operations is a vector space
SESSION 16
17
Mar
SESSION 16
Review
Review
Mon 8:30 PM - 9:15 PM UTCMar 17, 8:30 PM - 9:15 PM UTC
This is intended as a Linear Algebra Review Session before our Assessment or in between topics
SESSION 17
18
Mar
SESSION 17
Other Topics
Other Topics
Tue 8:30 PM - 10:00 PM UTCMar 18, 8:30 PM - 10:00 PM UTC
Norm, Inner Product, and Vector Spaces TEST (03/18)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 18
21
Mar
SESSION 18
Other Topics
Other Topics
Fri 8:30 PM - 10:00 PM UTCMar 21, 8:30 PM - 10:00 PM UTC
Basis, Dimension, and Subspaces DAY 1
1. Determine whether a vector is a linear combination of a given set; express a vector as a linear combination of a given set of vectors
2. Determine whether a set of vectors is linearly dependent or independent
3. Determine bases for n-dimensions of vector spaces/subspaces and give the dimension of the space
SESSION 19
24
Mar
SESSION 19
Other Topics
Other Topics
Mon 8:30 PM - 10:00 PM UTCMar 24, 8:30 PM - 10:00 PM UTC
Basis, Dimension, and Subspaces DAY 2
4. Prove or disprove that a given subset is a subspace of Rn
5. Reduce a spanning set of vectors to a basis
6. Extend a linearly independent set of vectors to a basis
SESSION 20
25
Mar
SESSION 20
Other Topics
Other Topics
Tue 8:30 PM - 10:00 PM UTCMar 25, 8:30 PM - 10:00 PM UTC
Basis, Dimension, and Subspaces DAY 3
7. Find a basis for the column space or row space and the rank of a matrix
8. Make determinations concerning independence, spanning, basis, dimension, orthogonality and orthonormality with regards to vector spaces
SESSION 21
28
Mar
SESSION 21
Review
Review
Fri 8:30 PM - 9:15 PM UTCMar 28, 8:30 PM - 9:15 PM UTC
This is intended as a Linear Algebra Review Session before our Assessment or in between topics
SESSION 22
31
Mar
SESSION 22
Other Topics
Other Topics
Mon 8:30 PM - 10:00 PM UTCMar 31, 8:30 PM - 10:00 PM UTC
Basis, Dimension, and Subspaces TEST (03/31)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 23
1
Apr
SESSION 23
Other Topics
Other Topics
Tue 8:30 PM - 10:00 PM UTCApr 1, 8:30 PM - 10:00 PM UTC
Linear Transformations DAY 1 04/01
1. Use matrix transformations to perform rotations, reflections, and dilations in Rn
2. Verify whether a transformation is linear
3. Perform operations on linear transformations including sum, difference and composition
Linear Transformations DAY 2 04/04
4. Identify whether a linear transformation is one-to-one and/or onto and whether it has an inverse
5. Find the matrix corresponding to a given linear transformation T: Rn -> Rm
6. Find the kernel and range of a linear transformation
Linear Transformations DAY 3 04/07
7. State and apply the rank-nullity theorem
8. Compute the change of basis matrix needed to express a given vector as the coordinate vector with respect to a given basis
REVIEW 04/08
Linear Transformations TEST (04/11)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 24
22
Apr
SESSION 24
Other Topics
Other Topics
Tue 8:30 PM - 10:00 PM UTCApr 22, 8:30 PM - 10:00 PM UTC
Eigenvalues and Eigenvectors DAY 1 04/22
1. Calculate the eigenvalues of a square matrix, including complex eigenvalues.
2. Calculate the eigenvectors that correspond to a given eigenvalue, including complex eigenvalues and eigenvectors.
Eigenvalues and Eigenvectors DAY 2 04/23-25 (if need be)
3. Compute singular values
4. Determine if a matrix is diagonalizable
5. Diagonalize a matrix
REVIEW 04/25 or 04/28
Eigenvalues and Eigenvectors TEST (04/28 or 04/29)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
SESSION 25
12
May
SESSION 25
Other Topics
Other Topics
Mon 8:45 PM - 10:45 PM UTCMay 12, 8:45 PM - 10:45 PM UTC
FINAL EXAM (05/30)
~2 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)