• Class Schedule: : TuTh 2:30-3:50, Library E4315

  • Syllabus

  • Exams
    •   Topic Worksheet Date Practice Problems Problems to hand in Homework due date
    Lecture 1 1.1. Introduction to linear systems Linear Systems Jan 26

    Section 1.1: 1, 3, 7, 9, 11, 31, 33

    Section 1.2: 1, 3, 5, 11

    Section 1.1: 2, 4, 8, 12

    Section 1.2: 4, 6, 8, 32

    Feb 9

    Lecture 2 1.2. Gauss-Jordan elimination and reduced row-echelon form  Gauss-Jordan and RREF Jan 28

    Lecture 3

    		1.3. On the solutions of Linear Systems solutions of linear systems Feb 2 Section 1.3: 1, 5, 9, 17, 23, 37, 45, 47, 58 Section 1.3: 2, 4, 14, 20, 22, 28

    Feb 16

     

    Lecture 4

    		2.1. Linear transformations linear transformations Feb 4

    Lecture 5

    		1.3. Matrix Algebra matrix algebra Feb 9
    Section 1.3: 11, 13, 27, 49, 55; 
    Section 2.1: 3, 5, 33; Section 2.2: 5
    Section 1.3: 12, 18, 34, 50, 56; 
    Section 2.1: 6, 32, 44; Section 2.2: 2, 32
    		Feb 23

    Lecture 6

    		2.2. Linear Transformations in Geometry geometry of linear transformations Feb 11

    Lecture 7

    		2.2. Linear Transformations in Geometry geometry of linear transformations Feb 16

    Section 2.1: 1, 19, 21, 42
    Section 2.2: 13, 17, 27( ignore shear), 53

    Section 2.3: 1, 7, 51

    Section 2.4: 3, 11

    Section 2.2: 10, 12, 26 (ignore part d), 30, 38 (a, b, c), 40

    Section 2.3: 2,50

    Section 2.4: 10, 38

    		March 1 

    Lecture 8

    		2.3 Matrix Multiplication matrix multiplication Feb 18

    Lecture 9

    		2.3-2.4: Matrix Multiplication, Inverse of a Linear Transformation inverse of linear transformations Feb 23

    Section 2.3: 5, 13, 17, 57, 65

    Section 2.4: 7, 19, 21, 31, 37

    Section 2.3: 8, 18, 56, 66

    Section 2.4: 2, 4, 20, 30, 42

    March 8 

     

     

    Lecture 10

    		2.4-3.1: Inverse of a Linear Transformation, Image and Kernel of a Linear Transformation

    Inverse, Image, and Kernel of a Linear Transformation 

    		Feb 25

    Lecture

    11

    		3.2: Subspaces of R^n; Bases and Linear Independence 

     

    Subspaces of R^n and Their Dimensions

     

    		March 1

    Section 3.1: 7, 11, 21

    Section 3.2: 3,29,  33

    Section 3.1: 8, 10, 22

    Section 3.2: 2, 4, 30, 32, 34

    and the problem in this link

    March 22

     

    Exam

    Midterm I

    (For the exam and its solutions go to the exam page)

     

    		March 3

    Lecture 12

    		3.2-3.3: Bases, Linear Independence and the Dimension of a Subspace of R^n  Subspaces of R^n and Their Dimensions II March 8

    Section 3.2: 23, 25, 31, 37

    Section 3.3: 7, 19, 25, 27

    Section 3.2: 23, 26, 30, 36

    Section 3.3: 6, 18, 24, 28

    		March 31

    Lecture 13

    		3.3: 

    The Dimension of a Subspace of R^n 

    		The Dimension of a Subspace of R^n March 10

    Lecture 14

    		3.3-3.4: The Dimension of a Subspace of R^n, Coordina 

    Bases and Coordinates for a Subspace of R^n

    		March 22

    Section 3.3: 29, 67, 87

    Section 3.4: 1, 17, 21, 29

    Section 3.3: 30, 36, 68, 86

     

    Section 3.4: 2,  18, 20, 28

    		April 5

    Lecture 15

    		3.4. Coordinates

     

    Coordinates

     

    		March 24

    Lecture 16

    		4.1 Introduction to Linear Spaces 

    Linear Spaces

    		March 29

    Section 4.1: 9, 17

    Section 4.2: 5, 7, 27

    Section 4.3: 61 (parts a and b)

    Section 4.1: 8, 16

    Section 4.2: 4, 6, 26

    Section 4.3: 60 (parts a and b)

    and the problems in this link

    		April 14

    Lecture 17

    		4.2 

    Linear Transformations and Isomorphisms

    Linear Transformations and Isomorphisms

    		March 31

    Lecture 18

    		4.3 The Matrix of a Linear Transformation Matrix of Linear Transformations April 5

    Section 4.1: 5

    Section 4.2: 67

    Section 4.3: 65

    Section 4.1: 2

    Section 4.2: 68

    Section 4.3: 64

    		April 21

    Lecture 19

    		5.1  Orthogonal Projections and Orthonormal Bases 

    Orthonormal Bases and Orthogonal Projections 

    		April 7

    Lecture 20

    5.1-5.2: Orthogonal Projections and Orthonormal Bases, Gram-Schmidt Process 

    Orthogonal Projections and Gram-Schmidt Process

    		April 12

    Section 5.1: 5, 11, 27

    Section 5.2: 5, 7, 13, 33

    Section 5.3: 3, 61

    Section 5.1: 6, 10, 26

    Section 5.2: 2, 6, 14, 32

    Section 5.3: 4, 60

    		April 28

    Lecture 21

    		5.3  Orthogonal Transformations and Orthogonal Matrices 

    Orthogonal Transformations and Transpose 

    		April 14

    Exam

    Midterm II

    (For the exam and its solutions go to the exam page)

    		  April 19

    Lecture 22

    		5.5 Inner Product Spaces

    Inner Product Spaces 

    		April 21

    Lecture 23

    6.1  Introduction to Determinants 

    Determinant of a Square Matrix 

    		April 26

    Section 6.1: 9, 17, 19, 39

    Section 6.2: 5

    Section 7.2: 3, 9, 11

    Section 7.3: 7, 9, 15

    Section 6.1: 8, 18, 20, 40

    Section 6.2: 6

    Section 7.2: 4, 8, 10

    Section 7.3: 8, 14, 16

    		May 5

    Lecture 24

    6.2-7.1  Properties of the Determinant, Diagonalization 

    Propoerties of Determinant and Diagonalizable Matrices

    		April 28

    Lecture 25

    7.2-7.3 Finding the Eigenvalues and the Eigenvectors of a Matrix 

     

    		May 3
    Lecture 26  

     

    		May 5