# MA 242 Linear Algebra

### Spring 2013

 Lecture MWF     9:00am – 10:00am     (MCS B33) Instructor Dr. Martina Chirilus-Bruckner Email martina.ma.242@gmail.com Office MCS 238 Phone (617) 353 - 1491         ! email preferred ! Discussion (C2) W     2:00pm – 3:00pm     (MCS B33) Office hours Special times during Final Exam week: Tuesday and Thursday 10-11am and 4-5pm

General course information: here

Announcements:
* Solutions to even HW problems are posted.
* FINAL EXAM: Friday, May 10, 12:30pm – 2:30pm (usual class room, MCS B33).

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 WEEK READING SUGGESTIONS ("Linear Algebra" David Lay, 4th edition) Homework DUE 01:   Jan 16/18 1.1: Systems of Linear Equations, 1.2 Row Reduction and Echelon Form EX 1 - 02:   Jan 23/25 1.2: Row Reduction and Echelon Form , 1.3 Vector Equations HW 1 January 30 03:   Jan 28/30, Feb 01 1.4-5: The Matrix Equation, Solution Set of Linear Systems HW 2 February 06 04:   Feb 04/06 1.5-7: Solution Set of Linear Systems, Applications, Linear Independence HW 3 February 13 05:   Feb 11/13/15 1.8-9, 2.1: Linear Transformation and its matrix, Matrix Operations *APPLICATION: matrix multiplication and image processing HW 4 February 20 06:   Feb 20/22 2.2-3: Inverse of a matrix and characterization of invertible matrices *HANDOUTS: Matrix Algebra, Invertible Matrices , Invertible Matrix Theorem HW 5 February 27 07:   Feb 25/27, March 01 2.3, 3.1, 3.3: Invertible linear transformations, Sarrus' rule, Cramer's rule *APPLICATIONS: Crytography, Fractals, Chemistry, Networks, *MATLAB CODE: fern.m, tree2.m HW 6 March 20 ------ March 04 ------ MIDTERM (in class) 08:   March 06/08 2.5, 3.1, 4.1 LU-decomposition, Determinants (Cofactor expansion), Vector Spaces, *HANDOUT: LU-decomposition EX 3 ---- March 09-17 ---- Spring Break 09:   March 18/20/22 3.2, 4.1, 4.2, 4.3: Determinants, Vector spaces, Null spaces, Linearly independent sets and Bases *HANDOUTS: Determinant (definition) , Determinant (properties) , 4-by-4 matrix example HW 7 March 27 10:   March 25/27/29 4.4, 4.5, 4.7, 5.1: Coordinate Systems, Dimension, Change of Basis, Eigenvectors and Eigenvalues *HANDOUT: Eigenvalues and eigenvectors *APPLICATION: Face recognition (Eigenfaces) HW 8 April 03 11:   April 01/03/05 5.2, 5.3, 7.1, 5.4: Characteristic Equation, Diagonalization, Eigenvectors and Linear Transformations *HANDOUT: Top 10 Algorithms in Science and Engineering *APPLICATION: Image Compression HW 9 April 10 12:   April 08/10/12 5.3, 5.4, 7.1, 5.8: Diagonalization, Eigenvectors and Linear Transformations, Iterative estimates of eigenvalues *HANDOUT: diag. (2 x 2 example) , diag. (3 x 3 example), *APPLICATION: Difference Equations HW 10 April 18 13:   April 17/18 6.1, 6.2: Inner Products, Length and Orthogonality, Orthogonal Sets*HANDOUT: Inner Product *APPLICATIONS (diagonalization): PageRank (full), PageRank (handout) HW 11 April 24 14:   April 22/24/26 6.3, 6.4 : Orthogonal Projections, Gram-Schmidt Process *HANDOUT: Gram-Schmidt * APPLICATIONS: Least-Squares, Fourier Series HW 12 May 02 ------ April 29, May 01 ------ REVIEW ---------- May 06-10 ---------- FINAL EXAM: Friday, May 10, 12:30pm – 2:30pm (usual class room, MCS B33).