Mr. Bly's Math 251 Webpage


Ayres 124
Section 6: TR 12:40-1:55
Section 1: TR 2:10-3:25

Final Exam Schedule
Section 6: Wed Dec 10 at 12:30-2:30
Section 1: Thu Dec 4 at 2:45-4:45

Office Hours
MWF 1:30-3:00pm Ayres 326

Email: bly@math.utk.edu




HW Help

Test 1
(Solutions)
HW for
Tue Aug 26
(Solutions)
(1) 1.1 #1
(2) 1.1 #11
(3) 1.1 #7
(4) Examples in class
(5) None
(6) Use x*y=1
Email Q&A
HW for
Thu Aug 28
(Solutions)
(1) 1.1 #9
(2) 1.2 #7
(3) 1.2 #25
(4) 1.2 #37
Email Q&A
HW for
Tue Sep 2
(Solutions)
(1) 1.2 #23c
(2) 1.2 #23abd
(3) 1.3 #9ab
(4) 1.3 #1abcde, #3i
(5) 1.2 #3
(6) 1.2 #39
(7) 1.3 #29
HW for
Thu Sep 4
(Solutions)
(1) 1.5 #3, #5
(2) 1.4 #37
(3) Similar to (2)
(4) 1.4 #23
Email Q&A
HW for
Tue Sep 9
(Solutions)
(1) 1.5 #13, #15, #17
(2) Technique from Thm
(3) 1.6 #15
(4) None
(5) 1.7 #9, #23
(6) Expand Thm
(7) None
Email Q&A
HW for
Thu Sep 11
(Solutions)
(1) 1.8 #1
(2) 1.8 #31
(3) 1.8 #13
(4) Properties from Thm
(5) Same as (4)
Email Q&A
HW for
Tue Sep 16
(Solutions)
(1) 2.1 #5, #7, #21, #31
(2) 2.2 #5, #7
(3) 2.3 #15, #17
(4) 2.3 #7, #9, #11, #13
(5) Result mimics determinant
(6) 2.1 #33
Email Q&A
HW for
Tue Sep 23
(Solutions)
(1) 2.2 #15, #17, #19
(2) 3.2 #1, #9
(3) 3.2 #11
(4) Elem Matrices?
(5) LHS and RHS separately?
Email Q&A
Test 2
(Solutions)
HW for
Thu Oct 2
(Solutions)
(1) Check Vector Space Axioms
(2) 4.2 #3
(3) Use Def of Span
(4) Use Def of Subspace
(5) None
Email Q&A
HW for
Tue Oct 7
(Solutions)
(1) 4.2 #11
(2) 4.2 #13
(3) 4.3 #5
(4) None
(5) 4.4 #3
(6) 4.4 #13
Email Q&A
HW for
Thu Oct 9
(Solutions)
(1) Apply Rephrased Original Thm
(2) Apply dim(V) Thm
(3) Apply dim(V) Thm
(4) a. is tricky, b. is dim(V) Thm
(5) Apply Rephrased Original Thm
Email Q&A
HW for
Tue Oct 14
(Solutions)
(1) 4.6 #9
(2) 4.9 #21
(3) None. (Make a picture?)
(4) None
(5) Apply Rephrased Original Thm
Email Q&A
HW for
Tue Oct 21
(Solutions)
(1) Use facts from notes
(2) 4.7 #11
(3) 4.7 #15, #17
(4) Location of zeros?
(5) Elem Matrices?
Email Q&A
HW for
Thu Oct 23
(Solutions)
(1) 4.8 #3, #5
(2) 4.8 #13
(3) 4.8 #3
(4) Original A^-1 Thm?
(5) Use facts from notes
Email Q&A
Test 3
(Solutions)
HW for
Tue Nov 4
(Solutions)
(1) 4.10 #21
(2) rank(T) & null(T) must be?
(3) 8.2 #32
(4) 4.2 #17
Email Q&A
HW for
Tue Nov 11
(Solutions)
(1) 8.1 #1
(2) Test Lin Trans Properties
(3) 8.3 #9
(4) Generic f in W looks like?
(5) 8.2 #29
Email Q&A
HW for
Thu Nov 13
(Solutions)
(1) 5.1 #13, #5
(2) 5.1 #7, #9, #11
(3) Geometric picture?
(4) 5.1 #29
(5) 5.1 #19(c)
Email Q&A
HW for
Tue Nov 18
(Solutions)
(1) 5.1 #7, #9, #11
(2) How many eigenvectors?
(3) 5.2 #7, #9
(4) 5.1 #31
(5) Mult A*x=lambda*x by A?
Email Q&A
HW for
Thu Nov 20
(Solutions)
(1) 7.1 #1, #3, #7
(2) Orthogonal = Isometric
(3) 5.2 #17
(4) Hints Given
Email Q&A


Weekly Quizzes

Test 1
Quiz Fri 8/29
Hints
Solutions
Quiz Fri 9/5
Hints
Solutions
Quiz Fri 9/12
Hints
Solutions
Quiz Thu 9/18
Hints
Solutions
Skills Checklist
Test 2
Quiz Fri 10/3
Hints
Solutions
Quiz Fri 10/10
Hints
Solutions
Quiz Wed 10/15
Hints
Solutions
Quiz Wed 10/23
Hints
Solutions
Skills Checklist
Test 3
Quiz Fri 11/7
Hints
Solutions
Quiz Fri 11/14
Hints
Solutions
Quiz Thu 11/20
Hints
Solutions
Skills Checklist
Final Exam
(Solutions)
Study Guide & Review Sheet


Khan Academy

Test 1
Thu 8/21
(Intro)
Elimination to Solve Equation Systems
Three-equation System (Row Method)
Linear Dependence/Independence (Row Method)
Intro to Vectors (Column Method)
Tue 8/26
(1.1 & 1.2)
Solving using an Augmented Matrix
Solving using an Augmented Matrix (free var)
Solving using an Augmented Matrix (no sol)
Thu 8/28
(1.2 & 1.3)
Multiplying Matrices
Transposing a Matrix
Tue 9/2
(1.4 & 1.5)
Is Matrix Multiplication Commutative?
Is Matrix Multiplication Associative?
The Identity Matrix
Thu 9/4
(1.6 & 1.7)
Inverting a 3x3 Matrix
Solving a System with Inverse Matrices
Tue 9/9
(1.8)
Transformations from R^n to R^m
Transformations and Matrices
Thu 9/11
(2.1-2.3)
Determinant of a 2x2 Matrix
Determinant of a 3x3 Matrix
Determinant of a Triangular Matrix
Tue 9/16
(3.1-3.2)
Real-valued Vectors
Norm & Dot Product
Thu 9/18
(3.2-3.3)
Angle Between Two Vectors
Projection of Vectors
Test 2
Thu 9/26
(4.1)
Vector Space Axioms (w/ explanation)
Vector Space Axioms (just the basics)
Tue 9/30
(4.2)
Subspaces
Span & Linear Combination
Thu 10/2
(4.3 & 4.4)
Linear Independence Example
Linear Dependence Example
Basis of a Vector Space
Tue 10/7
(4.5)
Vector Space Dimension
Thu 10/9
(4.6 & 4.9)
Coordinates for a given Basis
Reflection & Contraction/Dilation Matrices
Rotation Matrices
Tue 10/14
(4.7)
Null Space of a Matrix
Column Space of a Matrix
Tue 10/21
(4.8)
Rank of a Matrix
Nullity of a Matrix
Thu 10/23
(4.8 & 4.10)
Orthogonal Complements
im(T)
Onto Transformations
Test 3
Thu 10/30
(4.10 & 8.1)
1-to-1 Transformations
Invertible Transformations
Tue 11/4
(8.1 & 8.3)
Linear Transformations
Isomorphism
Tue 11/11
(5.1)
Intro to Eigenvalues/vectors
Eigenvalue Example
Eigenvector Example
Thu 11/13
(5.1 & 5.2)
Lin Ind of Eigenvectors & Diagonalization
Tue 11/18
(7.1)
Orthonormal Basis
Orthogonal Matrices & Isometries
Thu 11/19
(6.4 & 6.5)
When (A^T)*A is invertible
Least Squares Problem