Course: | MTH 1230, Linear Algebra (Seq. 10, Sec. 02, Key #02367) |
Instructor: | Prof. Alex Suciu |
Course Web Site: | www.math.neu.edu/~suciu/mth1230/linalg.sp01.html |
Time and Place: | Tue., Wed. & Fr., 11:45 AM -- 12:50 PM, in 302 KA |
Office Hours: | Tue., Wed. & Fr., 10:40 AM -- 11:40 AM, in 441 LA |
Prerequisites: | MTH 1223 (Calculus for Engineering majors 4) and MTH 1225 (Differential Equations 1) or equivalent |
Textbook: | Linear Algebra with Applications Second Edition, by Otto Bretscher, Prentice Hall, 2001 |
Grade: | 60% in-class exams, 40% final exam |
This course is an introduction to concepts, algorithms, theory, and applications of Linear Algebra. This subject is now recognized as being fully as important as Calculus in its range of applications. The course begins with methods for solving a system of linear equations in several unknowns. We will also learn how to find an approximate solution when no tru solution exists. We then proceed with the study of linear transformations and matrix operations, subspaces of n-dimensional space, images and kernels, bases and linear independence, orthonormal bases and QR-factorizations, with applications to least squares and data fitting. The course ends with a study of eigenvalues and eigenvectors, and uses these concepts to model change via difference equations. A further application of these ideas is the singular value decomposition of a matrix, which is useful in transmission of information. |
Section | Problems |
1.1: Linear systems and their geometry | 1, 7, 10, 20--22, 34 |
1.2: Matrices & Gaussian elimination | 2, 4, 5, 7, 17, 18, 20--22, 27, 29--31, 34, 35, 37, 41, 42 |
1.3: Solutions and matrices | 1--8, 10-15, 17--19, 21--32, 34--36, 47, 55 |
2.1: Linear transformations, inverses | 1--3, 5, 6, 9, 11, 24--30, 33, 35, 42 |
2.2: Geometry of linear transformations | 1, 3, 4, 6--10, 17, 19, 21, 23--26, 34, 43, 49 |
2.3: The inverse of a linear transformation | 1--5, 17, 19, 25, 35--41 |
2.4: Matrix products | 1--25 (odd only), 29, 47, 48, 49, 65, 76, 78 |
3.1: Subspaces, images and kernels | 1, 3, 5, 7, 10, 14, 15, 23, 25, 33, 35, 42, 53, 54 |
3.2: Bases and linear independence | 1, 3, 11--33 (odd only), 24, 37, 39, 46, 49, 52 |
3.3: Dimension of a subspace | 1, 3, 5, 7, 11, 13, 17, 21, 23, 27, 37, 39, 49, 52 |
5.1: Orthonormal bases and projections | 1, 3, 5, 13, 15, 17, 27, 31 |
5.2: Gram-Schmidt process & QR-factorization | 5, 7, 19, 21, 33, 35 |
5.3: Orthogonal matrices | 5--8, 13--18, 27--29 |
5.4 Least squares & data fitting | 8, 11, 13, 17--25, 31--33 |
6.1 Determinants | 1--11 (odd only), 17, 20, 27 |
6.2 Properties of determinants | 1, 4--10, 24--26, 31, 32, 37 |
6.3 Geometry of determinants | 2, 7, 9, 13, 14, 23 |
7.1 Eigenvectors, iteration of matices | 1--7, 9, 15--22, 34 |
7.2 Finding eigenvalues | 1--13 (odd only), 21, 28--31 |
7.3 Finding eigenvectors | 1--13 (odd only), 21, 40, 42, 43 |
7.4 Diagonalization and similarity | 1--9 (odd only), 18--22, 38--50 |
8.1 Symmetric matrices | 1, 3, 7 |
8.3 Singular value decomposition | 1--4, 17, 18 |
Geometry of linear transformations | Correlation coefficient | Gram-Schmidt process |
Exam 1 | Solutions to Exam 1 | |
Sample Exam 2 | Exam 2 | Solutions to Exam 2 |
Exam 3 | Solutions to Exam 3 | |
Sample Exam 4 | Exam 4 | Solutions to Exam 4 |
Final Exam | Alternate Final | Solutions to Final Exam |
An finally, here are the grades! |
Department of Mathematics | Office: | 441 Lake Hall | |
Northeastern University | Phone: | (617) 373-4456 | |
Boston, MA, 02115 | Email: | alexsuciu@neu.edu |
Started: March 27, 2001 Last modified: June 7, 2001
URL: http://www.math.neu.edu/~suciu/mth1230/linalg.sp01.html |