Home | Math Dept

 Here you will find information concerning the Linear Algebra (2270-1) class for the Spring 2003 Semester, which meets on Monday, Tuesday, Wednesday, and Friday 8:35AM-9:25AM in LCB 121. If you have any doubts, problems, concerns, etc., feel free to send a message to the instructor.

 Office Hours: I will be in my office Thursday 24 and Friday 25 from 8:30 to 12 noon waiting for your questions. If you can, send an email telling me at what time you are coming so that I know that you are coming. Final Exam: on Mon. 4/28, 8:00-10:00 AM, in the regular classroom. Homework 14 (post last homework) will neither be collected nor graded.

 4/23: Reviewed different ways of interpreting the invertibility of a square matrix. 4/22: Quadratic forms. Section 8.2. 4/21: Orthogonal diagonalization of matrices. Section 8.1. 4/18: More properties of diagonalizable matrices. Section 7.4 and some material not in the textbook. 4/16: Diagonalizable matrices, powers and exponential of (diagonalizable) matrices. Section 7.4. 4/15: Diagonalization. Sections 7.3 and 7.4. 4/14: Eigenbases. Section 7.3. 4/11: Multiplicities of eigenvalues. Eigenvectors. Sections 7.2 and 7.3. 4/9: Test 3 was given. 4/8: Some properties of eigenvalues. Section 7.2. 4/7: Eigenvalues and eigenvectors: definition and examples. Sections 7.1 and 7.2. 4/4: Introduction to eigenvalues and eigenvectors. Section 7.1. Also the third lab project was distributed. 4/2: Cramer's Rule and applications. Section 6.3. 4/1: More properties of the determinant, including relation with volume. Sections 6.2 and 6.3. 3/31: More properties of the determinant. Section 6.2. 3/28: Properties of the determinant. Section 6.2. 3/26: Example of orthogonal projection to trigonometric polynomials (Maple worksheet available). Definition of determinant for nxn matrices. Sections 5.5 and 6.1. Also, Test 3 was announced for Wednesday 4/9. 3/25: Inner product. Section 5.5. 3/24: Least square solutions. Maple worksheet available. Section 5.4. 3/14: orthogonal projections, orthogonal complements and least squares. Sections 5.3 and 5.4. 3/12: Orthogonal matrices. Section 5.3. 3/11: Orthogonal transformations. Section 5.3. 3/10: Gram-Schmidt orthogonalization and QR decomposition. Section 5.2. 3/7: Some remarks on Test 2. Inequalities involving the dot product and angle between vectors. Section 5.1. 3/5: Test 2 was given. 3/4: orthogonal projection and complement. Section 5.1. 3/3: Length and orthogonality in R^n. Section 5.1. 2/28: Matrix of a linear transformation. Section 4.3. Also, the second lab project was distributed and is due on Friday 3/14. 2/26: Coordinates. Section 4.3. 2/25: Properties of isomorphisms. Section 4.2. 2/24: Linear transformations, isomorphisms and isomorphic spaces. Section 4.2. 2/21: Bases. Linear transformations. Sections 4.1 and 4.2. Test 2 was announced for 3/5. 2/19: Subspaces, bases, examples. Section 4.1. 2/18: Notion of vector space and examples. Section 4.1. 2/14: Matrix of a linear transformation with respect to different bases. Section 3.4. 2/12: Matrix of a linear transformation. Section 3.4. 2/11: Bases of R^n. Coordinates. Sections 3.3 and 3.4. 2/10: Dimension of the kernel and image of a linear transformation. Section 3.3. 2/7: Dimension of a subspace. Section 3.3. 2/5: Basis of a subspace. Section 3.2. 2/4: More examples of subspaces. Linear independence of vectors. Section 3.2. 2/3: Properties of the kernel. Notion of subspaces of R^n. Sections 3.1 and 3.2. 1/31: Remarks on Test 1. Continued discussion of the image of a linear transformation and notion of kernel. Section 3.1. 1/29: Test 1 was given. 1/28: Discussed some problems from the practice test and continued the discussion of the image of a linear transformation. Section 3.1. 1/27: Some properties of matrix multiplication. Notion of image of a linear transformation. Sections 2.4 and 3.1. 1/24: Matrix multiplication and composition of linear transformations. Section 2.4. 1/22: Second lab session. The material is covered by this tutorial and we distributed the first lab project, that is due on Wed 2/5. 1/21: Inverse linear transformations and inverse matrices. Section 2.3. 1/17: Review of dot product in R^n. Orthogonal projections. Inverse linear transformations. Sections 2.2 and 2.3. Also Test 1 was announced. 1/15: We had a computer lab where we covered an introductory Maple tutorial. 1/14: Examples of linear transformations. Dilations and rotations. Section 2.2. 1/13: Matrix operations (sum, difference and multiplication by scalar). Notion of linear transformation. Sections 1.3 and 2.1. 1/10: Vector and matrix form of a linear system. Linear combinations and product of a matrix by a vector. Section 1.3. Homework 1 was assigned. 1/8: Reduced Row Echelon Form: properties and applications. Sections 1.2 and 1.3. 1/7: Matrices and Gauss-Jordan elimination. Section 1.2. 1/6: Discussion of the "technical" aspects of this class (full information in the syllabus. Solving a system of linear equations and the geometric interpretation. Section 1.1.

 Rules: all exercises posted in this section are for your use. Homework due is explicitly marked below with the corresponding due date. Include complete discussion for the True/False exercises. Homework 14: Will neither be collected nor graded. (7.4) 6, 16, 22, 38, 58; (8.1) 8, 10, 12; (8.2) 2, 6, 10. Homework 13: Due Friday 4/18 (only the un-starred exercises) . (7.2) 4, 10, 12, 20; (7.3) 6, 12, 16, 26, 36, 44*. Homework 12: Due Friday 4/11. Include complete discussion for the True/False exercises. (6.2) 2, 10, 12, 24; (6.3) 2, 10, 24; (True/False) 2, 4, 10, 20; (7.1) 2, 4, 8, 20. Homework 11: Due Friday 4/4. Include complete discussion for the True/False exercises. (5.4) 20, 22, 24; (5.5) 8, 10, 16; (True/False) 4, 10, 30; (6.1) 6, 14, 16, 24, 28. Homework 10: Due Friday 3/28. (5.3) 2, 6, 10, 14, 16, 20. Homework 9: Due Friday 3/14 (only the un-starred exercises). (5.1) 6, 10, 14*, 16, 28; (5.2) 14, 18, 32, 34. Homework 8: Due Friday 3/7 (only the un-starred exercises). (4.3) 2, 14, 20, 24, 36, 54, 64*. Homework 7: Due Friday 2/28 (only the un-starred exercises). (4.1) 2, 4, 6, 10, 14, 16, 26, 28; (4.2) 4, 6, 14, 16, 28, 38, 42, 44*. Homework 6: Due Friday 2/21 (only the un-starred exercises). Include complete discussion for the True/False exercises. (3.4) 2, 6, 8, 12, 14, 18, 30, 32*, 34; (True/False) 4, 6, 14, 30. Homework 5: Due Friday 2/14. (3.2) 2, 6, 8, 16, 28; (3.3) 4, 8, 14, 20, 22, 24, 28, 30. Homework 4: Due Friday 2/7 (only the un-starred exercises) (3.1) 4, 8, 14, 16, 32, 34, 37, 53*, 54*. Homework 3: Due Friday 1/31 (only the un-starred exercises) (2.4) 4, 10, 12, 16, 20, 28, 80*; (True/False) 8, 12, 20. Homework 2: Due Friday 1/24 (only the un-starred exercises) (2.1) 5, 24 - 30, 42; (2.2) 2, 6, 28; (2.3) 2, 6, 20, 34, 45*. Homework 1: Due Friday 1/17 (only the un-starred exercises) (1.1) 2, 6, 12, 14, 25; (1.2) 4, 6, 18, 24, 30, 40*; (1.3) 1, 2, 4, 6, 14, 18; (True/False) 2, 3, 9.

Below you will find different references on the course (syllabus, etc.).

 (Home-Made) Maple Tutorials: first tutorial (PDF and PS versions). second tutorial (PDF and PS versions). third tutorial (PDF and PS versions). fourth tutorial (PDF and PS versions). Lab Projects: third project (also in PDF and PS formats). For this project you need to download the file proj3data.m. Solution: Maple worksheet and PDF file. second project (also in PDF and PS formats). For this project you need to download the file proj2data.m. Solution: Maple worksheet and PDF file. first project (also in PDF and PS formats). Assorted comments: In exercise 2, the T-nodes have a fixed temperature that is not controlled by averaging (which only "affects" the P- and N- nodes). In exercise 2b you have to find an expression for the temperature at the P-nodes in terms of the temperature at the T-nodes (remember that the T-nodes have fixed temperature). Solution: Maple worksheet and PDF file. Trigonometric Polynomials: Maple worksheet and PDF file. Least Squares: Maple worksheet and PDF file. The syllabus (also in PDF and PS formats). Here you will find the "ultimate" guidelines for the course, textbook, schedule, final exam, etc. Short questionnaire (also in PDF and PS formats) that you should print out, complete and return to the instructor.

 Maple web site. Here are some tutorials. Official academic calendar, Spring 2003. Student Handbook. General Catalog. Campus map and building locator. University of Utah homepage. Mathematics undergraduate colloquium.

Home | Math Dept