# 21-241: Matrix Algebra

### Schedule and Homework

For each week there will be a link to a page with a reading assignment and a homework assignment.

This schedule is tentative. It will get more accurate as the semester progresses. As each topic is covered in lecture, the color will be changed from blue to black.

 Week #1:  Jan 10 - 14 Homework 1.1. Systems of Linear Equations. 1.2. Row Reduction and Echelon Forms. 1.3. Vector Equations. Week #2:  Jan 17 - 21 Homework 1.4. The Matrix Equation Ax = b. 1.5. Solution Sets of Linear Systems. Administrative Note: Monday 6 September is Labor Day. Class will not meet. Week #3:  Jan 24 - 28 Homework 1.7. Linear Independence. 1.8. Introduction to Linear Transformations. 1.9. The Matrix of a Linear Transformation. Week #4:  Jan 31 - Feb 4 Homework 2.1. Matrix Operations. 2.2. The Inverse of a Matrix. 2.3. Characterizations of Invertible Matrices. Week #5:  Sep. 27 - Oct. 1 Homework 2.5. Matrix Factorizations. 2.7. Applications to Computer Graphics. Exam #1 will be given on Wednesday 29 September. The exam will be held during your regular class time. Here are some review problems. Week #6:  Oct. 4 - 8 Homework 3.1. Introduction to Determinainants. 3.2. Properties of Determinants. 4.1. Vector Spaces and Subspaces. Week #7:  Oct 11 - 15 Homework 4.2. Null Spaces, Column Spaces, and Linear Transformations. 4.3. Linearly Independent Sets; Bases. 4.4. Coordinate Systems. Week #8:  Oct 18 - 22 Homework 4.5. The Dimension of Vector Space. 4.6. Rank. Administrative note: Friday 22 October is the Mid-Semester Break. Class will not meet. Week #9:  Oct 25 - 29 Homework 4.7. Change of Basis. 4.9. Applications to Markov Chains. Exam #2 will be given on Wednesday 27 October. Here are some review problems. Week #10:  Nov 1 - 5 Homework 5.1. Eigenvectors and Eigenvalues. 5.2. The Characteristic Equation. 5.3. Diagonalization. Week #11:  Nov 8 - 12 Homework 5.4. Eigenvectors and Linear Transformations. 5.5. Complex Eigenvalues. 5.6. Discrete Dynamical Systems. Week #12:  Nov 15 - 19 Homework 6.1. Inner Product, Length, and Orthogonality. 6.2. Orthogonal Sets. 6.3. Orthogonal Projections. Week #13:  Nov 22 - 26 Homework Exam #3 will be given on Monday 22 November. Here is a study guide. Administrative Note: Wednesday -- Friday the 24 - 26 of November is the Thanksgiving Holiday. Class will not meet. Here is a study guide. More items may be added, so check back. Week #14:  Nov 29 - Dec 3 Homework 6.4. The Gram-Schmidt Process. 6.5. Least-Squares Problems. 7.1. Diagonalization of Symmetric Matrices. Week #15:  Dec 6 - 10 Homework 7.2. Quadratic Forms. 7.4. The Singular Value Decomposition. 7.5. Applications to Image Processing and Statistics. Administrative note: Friday 10 December is the last day of class. Final Exam Dec 14 Final Exams. Our final exam has been scheduled for Tuesday 14 December, from 1:00-4:00. Section A and B will take the exam in MM103, Sections C and D in MM A14 and Section E in DH 2109. When making your travel plans, you should make sure there is no need for you to leave campus before 4:00pm on December 14. Here are some review problems.

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