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Math 4153
Finite Dimensional Vector spaces
TextBook: Linear Algebra --- S. Friedberg, A. Insel, and L. Spence.
Office Hours: M 11:30 -12:30 and Th 1:45 - 3 at 246 Lockett
If the office hours do not work for you, please send us emails to make an appointment.
Office Hours: M 11:30 -12:30 and Th 1:45 - 3 at 246 Lockett
If the office hours do not work for you, please send us emails to make an appointment.
Homework: 15
Midterm: 60, Sep 21, Oct 19, Nov 21
Final: 25, Due on 12:00 pm, Dec 7 2018.
Midterm: 60, Sep 21, Oct 19, Nov 21
Final: 25, Due on 12:00 pm, Dec 7 2018.
Outline:
Chapter I: Vector Spaces
Section 1.2: Vector Spaces (Exercise: 1, 2, 7, 9, 11, 13, 21)
Section 1.3: Subspaces (Exercise: 1, 8, 11, 18, 19, 20, 23)
Section 1.4 & 1.5: Linear Combinations and Linear Independence
Sec 1.4: 1, 3, 4, 9, 10, 13, 14, 16;
Sec 1.5: 1, 4, 5, 6
Section 1.6: Bases and Dimension (Exercise: 1, 2, 3, 14, 15, 16, 22, 23, 29, 30)
Chapter 2: Linear Transformations and Matrices
Section 2.1: Linear Transformations (Exercise: 1, 4, 6, 11, 14, 14, 20)
Section 2.2-2.5: Matrices
Sec 2.2: 1, 3, 4, 5, 11
Sec 2.3: 1, 3, 11, 13 ( T_0 stands for the zero transformation)
Sec 2.4: 1, 3, 10, 14, 15, 17, 21, 24
Sec 2.5: 2, 3, 4, 5, 6, 7
Section 4.1-4.4: Determinants
Chapter 5: Diagonalization
Section 5.1: Eigenvalues and Eigenvectors (Exercies: 2, 7, 8, 15, 17)
Section 5.2: Diagonalizability and Direct Sums (Exercies: 1, 2, 3, 8, 12, 17, 18)
Section 5.3: Cayley-Hamilton Theorem
Chapter 6: Inner Product Spaces
Section 6.1 & 6.2: Inner Products, the Gram-Schmidt Process and Orthogonal Complements
Sec 6.1: 1, 3, 4, 5, 11, 15, 17, 18, 24
Sec 6.2: 2(c)(d), 6, 9, 18
Chapter I: Vector Spaces
Section 1.2: Vector Spaces (Exercise: 1, 2, 7, 9, 11, 13, 21)
Section 1.3: Subspaces (Exercise: 1, 8, 11, 18, 19, 20, 23)
Section 1.4 & 1.5: Linear Combinations and Linear Independence
Sec 1.4: 1, 3, 4, 9, 10, 13, 14, 16;
Sec 1.5: 1, 4, 5, 6
Section 1.6: Bases and Dimension (Exercise: 1, 2, 3, 14, 15, 16, 22, 23, 29, 30)
Chapter 2: Linear Transformations and Matrices
Section 2.1: Linear Transformations (Exercise: 1, 4, 6, 11, 14, 14, 20)
Section 2.2-2.5: Matrices
Sec 2.2: 1, 3, 4, 5, 11
Sec 2.3: 1, 3, 11, 13 ( T_0 stands for the zero transformation)
Sec 2.4: 1, 3, 10, 14, 15, 17, 21, 24
Sec 2.5: 2, 3, 4, 5, 6, 7
Section 4.1-4.4: Determinants
Chapter 5: Diagonalization
Section 5.1: Eigenvalues and Eigenvectors (Exercies: 2, 7, 8, 15, 17)
Section 5.2: Diagonalizability and Direct Sums (Exercies: 1, 2, 3, 8, 12, 17, 18)
Section 5.3: Cayley-Hamilton Theorem
Chapter 6: Inner Product Spaces
Section 6.1 & 6.2: Inner Products, the Gram-Schmidt Process and Orthogonal Complements
Sec 6.1: 1, 3, 4, 5, 11, 15, 17, 18, 24
Sec 6.2: 2(c)(d), 6, 9, 18
Homework Assignments: (The problems that you have to turn in.)
Due on 8/31: Sec 1.2: 9, 13, 21
Due on 9/7: Sec 1.3: 18, 19, 23
Due on 9/14: Sec 1.4: 10, 14, 16
Due on 9/19: Sec 1.6: 14, 30
Due on 9/24: Sec 1.6: 29
Due on 10/8: Sec 2.1: 6, 13, 20
Due on 10/12:Sec 2.2: 11; Sec 2.3: 11; Sec 2.4: 14, 15
Due on 10/22: Sec 2.5: 7
Due on 10/26: Sec 5.1: 8, 17
Due on 11/2: Prove Theorem 5.7, Sec 5.2: 2 (a) (b), 3(b), 8, 12
Due on 11/9: Prove Theorem 5.21, Sec 5.4: 6 (a) (c), 11, 24
Due on 11/16: Sec 6.1: 3, 5, 15, 17; Sec 6.2: 9
Due on 8/31: Sec 1.2: 9, 13, 21
Due on 9/7: Sec 1.3: 18, 19, 23
Due on 9/14: Sec 1.4: 10, 14, 16
Due on 9/19: Sec 1.6: 14, 30
Due on 9/24: Sec 1.6: 29
Due on 10/8: Sec 2.1: 6, 13, 20
Due on 10/12:Sec 2.2: 11; Sec 2.3: 11; Sec 2.4: 14, 15
Due on 10/22: Sec 2.5: 7
Due on 10/26: Sec 5.1: 8, 17
Due on 11/2: Prove Theorem 5.7, Sec 5.2: 2 (a) (b), 3(b), 8, 12
Due on 11/9: Prove Theorem 5.21, Sec 5.4: 6 (a) (c), 11, 24
Due on 11/16: Sec 6.1: 3, 5, 15, 17; Sec 6.2: 9
