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Linear Algebra and Matrix Theory

by Kiryl Tsishchanka

SYLLABUS
GRADE CALCULATOR
WolframAlpha
Reviews
Tests
Weeks Dates Sections Handouts  Homework
Due Dates
Mandatory Recommended
1
Jan 16, 18
Section 1.1 Fundamental Operations with Vectors
4(b), 5(d), 8(d), 9 1-20
Jan 25
Section 1.2 The Dot Product
2, 3, 10, 15(b)
1-20
2
Jan 23, 25 Section 1.3 An Introduction to Proof Techniques
1(a), 2(a), 3, 4, 6(b), 12, 13, 22, 23
1-7, 11-17, 21-24
Feb 1
3
Jan 30, Feb 1 Section 1.4
Fundamental Operations with Matrices
4, 5(a)-(c), 13
1-13, 15
Feb 8
Section 1.5 Matrix Multiplication
6, 13, 21, 22
1-25, 31
Section 2.1
Solving Linear Systems Using Gaussian Elimination
1(d), 5, 10
1-11
4
Feb 6, 8 Section 2.2
Gauss-Jordan Row Reduction and Reduced Row Echelon Form
2(d), 5(d), 7(b), 11(a),(c),(d), 13
1-14
Feb 15
Section 2.3
Equivalent Systems, Rank, and Row Space
8(d), 9(b), 16, 18
1-22
5
Feb 13, 15
Section 2.4
Inverses of Matrices
4(b), 9, 18
1-22
Feb 22
Section 3.1
Introduction to Determinants
8, 11(b), 16(a)
1-18
Section 3.2
Determinants and Row Reduction
2(d), 4(b), 7
1-16
6
Feb 20, 22
Section 3.3 Further Properties of the Determinant 4(b), 6(b), 8(a), 10, 12
1-22
Mar 1
Section 3.4
Eigenvalues and Diagonalization 3(f), 5(b), 11, 17
1-20, 24
7
Feb 27
Section 4.1 Introduction to Vector Spaces 2-4, 6, 7, 9, 10, 15, 18
1-20
Mar 8
Mar 1
Sections 1.1-1.5, 2.1-2.4, 3.1-3.4
MIDTERM 1


8
Mar 6, 8
Section 4.2 Subspaces 1(i), 2(d), 3(d), 6, 11
1-22
Mar 22
9
Mar 12-17 Spring break
10
Mar 20, 22
Section 4.3 Span 2(b), 3(b), 9, 10, 12, 15, 19 1-29 Mar 29
Section 4.4 Linear Independence 3(b), 5, 8, 12, 17, 18
1-28
11
Mar 27, 29 Section 4.5 Basis and Dimension 2, 3, 4(d), 7, 15(a) 1-25
Apr 5
Section 4.6 Constructing Special Bases 1(b), 4(f), 5(b), 6(d), 12(a) 1-20
12
Apr 3 Section 4.7 Coordinatization 1(i), 2(b), 4(d), 12, 14, 15 1-16
Apr 12
Apr 5
Sections 4.1-4.7 MIDTERM 2


13
Apr 10, 12
Section 5.1 Introduction to Linear Transformations 1(e, g), 5, 7, 16, 19 1-36 Apr 19
Section 5.2 The Matrix of a Linear Transformation 2(d), 3(d), 7(b), 14 1-3, 7-9, 13, 14
14
Apr 17, 19
Section 5.3 The Dimension Theorem 1(b), 2(b), 3(b), 4(h), 13 1-20
Apr 26
Section 5.4 One-to-One and Onto Linear Transformations 1(d),(f), 2(d), 5, 6 1-9
15
Apr 24, 26 Section 5.5 Isomorphism 1(b), 3, 4, 12 1-23 May 3
Section 6.1
Orthogonal Bases and the Gram-Schmidt Process
1(d), 2(b), 3(b), 4(d), 5(b), 7(b), 10
1-22
16
May 1, 3
Section 6.2 Orthogonal Complements
1(c, d), 2(c), 4(b, c), 11, 14, 21
1-4, 11-26
Section 6.3
Orthogonal Diagonalization



17
May 11 (Fri) 2:00-5:00pm Cumulative FINAL EXAM