Mr. Bly's Math 251 Webpage


bly@math.utk.edu


Class Meetings (MTWRF)
1:30-3pm Ayres 124

Office Hours (MTWRF)
11:15am-12:15pm Ayres 326




Math Tutorial Center

Ayres G012
Mon: 11am-3pm
Tue: 11am-3pm
Wed: 11am-3pm
Thu: 11am-3pm

Hodges North Commons
Tue: 6-8pm
Thu: 6-8pm


HW Help

Test 1
HW for
Tue Jun 2
(Solutions)
(1) 1.2 #3d
(2) 1.2 #5
(3) 1.2 #3
HW for
Wed Jun 3
(Solutions)
(1) 1.3 #1
(2) 1.3 #5a-h
(3) 1.3 #5a-h
(4) 1.4 #37
Email Q&A
HW for
Thu Jun 4
(Solutions)
(1) 1.5 #13, #15
(2) 1.6 #3, #5
(3) Thm 1?
HW for
Fri Jun 5
(Solutions)
(1) None
(2) 1.7 #13
(3) 2.1 #29
(4) 2.2 #1, #3
(5) 2.2 #21, #25
Email Q&A
HW for
Mon Jun 8
(Solutions)
(1) 2.1 #27, #29
(2) 2.2 #15, #17, #19, #21
(3) Thm 1?
(4) Thm 1?
HW for
Tue Jun 9
(Solutions)
(1) 3.1 #9
(2) None
(3) 1.3 #9
(4) 1.8 #11
Test 2
HW for
Fri Jun 12
(Solutions)
(1) 4.1 #1e
(2) 4.1 #5
(3) 4.1 #1e
(4) 4.2 #2b
(5) 4.2 #1a
(6) 4.2 #2d
(7) 4.2 #17
Email Q&A
HW for
Mon Jun 15
(Solutions)
(1) Write out linear combo=0. Exploit zero vector to find a nonzero sol'n.
(2) Same as (1), but w/ sin^2 and cos^2.
(3) The key is the 12 entry.
(4) Write out linear combo. Section 1.7?
(5) One vector per unique choice of entry?
HW for
Tue Jun 16
(Solutions)
(1) 4.4 #5
(2) Remove a dependent column vector from gen{col vectors}
(3) 4.5 #9
HW for
Wed Jun 17
(Solutions)
(1) 4.4 #2
(2) 4.6 #3b
(3-4) See explanation to right
Email Q&A
HW for
Thu Jun 18
(Solutions)
(1-2) 4.7 #7
(3) Use column relations in rref
(4) You can see what columns form a basis in rref(A)'s column space. Now, relate this to A.
(5) Recall what transposing a matrix does
HW for
Fri Jun 19
(Solutions)
(1) 4.7 #11
(2) 4.8 #9, #21
(3) Thm 1?
Test 3
HW for
Wed Jun 24
(Solutions)
(1) 5.1 #1, #3
(2) 5.1 #11, #13
(3) 5.1 #5
Email Q&A
HW for
Thu Jun 25
(Solutions)
(1) 5.1 #7, #11
(2) Hint given
(3) Each value has at least one vector...
(4) 5.1 #7, #11
(5) Thm 4 tells you what D looks like.
HW for
Fri Jun 26
(Solutions)
(1) 5.1 #1, #3
(2) 5.2 #5, #7
(3) 5.2 #19
(4) nullity(A-cI) is number of eigenvectors you'll get for the eigenvalue c, right?
After Test 3
HW for
Wed Jul 1
(1) 6.4 #30
(2) 6.5 #3
(3) 2.3 #39
(4) 2.3 #39


Weekly Quizzes

Test 1
(Solutions)
Quiz Wed 6/3
Hints
Solutions
Quiz Fri 6/5
Hints
Solutions
Quiz Wed 6/10
Hints
Solutions
Skills Checklist
Test 2
(Solutions)
Quiz Fri 6/12
Hints
Solutions
Quiz Wed 6/17
Hints
Solutions
Quiz Fri 6/19
Hints
Solutions
Skills Checklist
Test 3
(Solutions)
Quiz Wed 6/24
Hints
Solutions
Quiz Fri 6/26
Hints
Solutions
Skills Checklist
Final Exam
(Solutions)
Final Review


Khan Academy

Test 1
Mon 6/1
(1.1, 1.2)
The HS Alg thought underlying Matrix Alg
Elem Row Ops on an Augmented Matrix
Elem Row Ops on an Augmented Matrix (free var)
Elem Row Ops on an Augmented Matrix (no sol)
Tue 6/2
(1.3, 1.4)
Transposing a Matrix
Adding & Subtracting Matrices
Multiplying a Matrix by a Scalar
Multiplying a Matrix by another Matrix
Is Matrix Multiplication Commutative?
The Identity Matrix
Wed 6/3
(1.5, 1.6)
Inverting a 3x3 Matrix
Solving a System with Inverse Matrices
Thu 6/4
(1.7, 2.1)
Determinant of a 2x2 Matrix
Determinant of a 3x3 Matrix
Determinant of a Triangular Matrix
Fri 6/5
(2.2, 2.3)
Determinant and multiplying a row by a scalar
Mon 6/8
(3.1, 1.8)
Real-valued Vectors
Transformations from R^n to R^m
Matrix Transformations
Tue 6/9
(3.2)
Norm & Dot Product
Angle Between Two Vectors
Test 2
Thu 6/11
(4.1, 4.2)
[Youtube] General Vector Space Explanation
[Youtube] The Vector Space Axioms
Subspaces
Fri 6/12
(4.2, 4.3)
Null Space Intro
Column Space Intro
Linear Independence Example
Linear Dependence Example
Mon 6/15
(4.4, 4.5)
Basis of a Vector Space
Vector Space Dimension
Tue 6/16
(4.6)
Coordinates for a given Basis
Wed 6/17
(4.7)
dim(col(A))
nullity(A)
Thu 6/17
(4.8)
None
Fri 6/18
(4.9, 4.10)
Image of a Transformation
When a matrix transformation is onto
Test 3
Tue 6/23
(5.1)
Intro to Eigenvalues/vectors
Eigenvalue Example
Eigenvector Example
Wed 6/24
(5.2)
Lin Ind of Eigenvectors & Diagonalization
Thu 6/24
(5.2 & 7.1)
None
Fri 6/25
(7.1 & 7.2)
Orthonormal Basis
Orthogonal Matrices & Rigid Transformations
After Test 3
Tue 6/30
(6.4+)
Least Squares Approximation
Least Squares Example