Introduction to Linear Algebra MAT 211 (LEC 3) Spring 2009
Mathematics department
Julia Viro

Generalities	Instructors	Schedule	Homework	Exams	Help

 

Day of	Contents	Sections
1/27, 1/29	Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. Gauss-Jordan elimination.	1.1-1.2
2/3, 2/5	Matrix vocabulary. Operations on matrices. Space Rn. Rank of a matrix. Number of solutions of a linear system.	1.2-1.3
2/10, 2/12	Linear transformations from Rm to Rn. Matrix of a linear transformation. Linear transformations in a plane: scalings, projections, reflections, rotations, shears. Composition of linear transformations and matrix product. Inverse linear transformation and invertible matrices.	2.1-2.4
2/17, 2/19	Subspaces of Rn. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension.	3.1-3.4
2/24, 2/26	Kernel and image of a linear transformation. Kernel- Image (Rank-Nullity) theorem.	3.3
3/3	Review for Midterm I.	1.1-3.4
Thursday 3/5	Midterm I
3/10, 3/12	Linear transformations and their matrices. Isomorphisms. Change of a basis.	4.2-4.3
3/17, 3/19	Inner product spaces. Euclidean space Rn. Orthogonality. Orthonormal bases. Orthogonal projections. Orthogonal complement.	5.1
3/23-3/27	Cauchy-Schwarz inequality, triangle inequality. Gram-Schmidt orthogonalization and QR-factorization.Orthogonal transformations and orthogonal matrices.	5.2-5.3, 5.5
3/31	Review for Midterm II.	4.1-4.3, 5.1-5.3, 5.5
Thursday 4/2	Midterm II	4.1-4.3, 5.1-5.3, 5.5
4/6-4/10	Spring recess
4/14, 4/16	Determinants and their geometrical interpretation. Properties of determinants.	6.1-6.3
4/21, 4/23	Eigenvalues and eigenvectors. Eigenspaces.	7.1-7.3
4/28, 4/30	Characteristic equation. Algebraic and geometric multiplicity of an eigenvalue. Eigenbasis. Diagonalization.	7.4
5/5, 5/7	Review for Final.
Tuesday 5/12 12:00-1:30 in P131 (Math Tower)	Extra review for Final
Tuesday 5/19 11:00am-1:30pm	Final exam