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Linear Algebra and Matrix Theory

by Kiryl Tsishchanka

SYLLABUS
GRADE CALCULATOR
WolframAlpha
Tests

Weeks Dates Sections Handouts  Homework
Due Dates
Mandatory Recommended
1
Aug 30, Sep 1
Section 1.1 Fundamental Operations with Vectors
4(b), 5(d), 8(d), 9 1-20
Sep 8
Section 1.2 The Dot Product
2, 3, 10, 15(b)
1-20
2
Sep 6, 8 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
Sep 15
3
Sep 11, 13, 15 Section 1.4
Fundamental Operations with Matrices
4, 5(a)-(c), 13
1-13, 15
Sep 22
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
Sep 18, 20, 22 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
Sep 29
Section 2.3
Equivalent Systems, Rank, and Row Space
8(d), 9(b), 16, 18
1-22
5
Sep 25, 27, 29
Section 2.4
Inverses of Matrices
4(b), 9, 18
1-22
Oct 6
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
Oct 2, 4, 6 Section 3.3 Further Properties of the Determinant 4(b), 6(b), 8(a), 10, 12
1-22
Oct 13
Section 3.4
Eigenvalues and Diagonalization 3(f), 5(b), 11, 17
1-20, 24
7
Oct 9, 11 Section 4.1 Introduction to Vector Spaces 2-4, 6, 7, 9, 10, 15, 18
1-20
Oct 20
Oct 13
Sections 1.1-1.5, 2.1-2.4, 3.1-3.4
MIDTERM 1


8
Oct 16, 18, 20
Section 4.2 Subspaces 1(i), 2(d), 3(d), 6, 11
1-22
Oct 27
Section 4.3 Span 2(b), 3(b), 9, 10, 12, 15, 19
1-29
9
Oct 23, 25, 27
Section 4.4 Linear Independence

Nov 3
Section 4.5 Basis and Dimension

10
Oct 30, Nov 1, 3
Section 4.6 Constructing Special Bases

Nov 10
Section 4.7 Coordinatization

11
Nov 6, 8
Section 5.1 Introduction to Linear Transformations

Nov 17
Nov 10
Sections 4.1-4.7 MIDTERM 2


12
Nov 13, 15, 17
Section 5.2 The Matrix of a Linear Transformations

Dec 1
Section 5.3 The Dimension Theorem

13
Nov 20 Section 5.4 One-to-One and Onto Linear Transformations

Dec 1
Nov 22-25 Thanksgiving holidays


14
Nov 27, 29, Dec 1
Section 5.5 Isomorphism

Dec 8
Section 5.6 Diagonalization of Linear Operators

15
Dec 4, 6, 8 Section 6.1
Orthogonal Bases and the Gram-Schmidt Process


Dec 11
Section 6.2 Orthogonal Complements


16
Dec 11
Section 6.3
Orthogonal Diagonalization



17
Dec 15 (Fri) 2:00-5:00pm Cumulative FINAL EXAM