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.

• (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.