Introduction to Linear AlgebraMAT 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. GaussJordan elimination.  1.11.2 
2/3, 2/5  Matrix vocabulary. Operations on matrices. Space R^{n}. Rank of a matrix. Number of solutions of a linear system.  1.21.3 
2/10, 2/12  Linear transformations from R^{m} to R^{n}. 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.  2.12.4 
2/17, 2/19  Subspaces of R^{n}. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension.  3.13.4 
2/24, 2/26  Kernel and image of a linear transformation. Kernel Image (RankNullity) theorem.  3.3 
3/3  Review for Midterm I.  1.13.4 
Thursday 3/5  Midterm I  
3/10, 3/12  Linear transformations and their matrices. Isomorphisms. Change of a basis.  4.24.3 
3/17, 3/19  Inner product spaces. Euclidean space R^{n}. Orthogonality. Orthonormal bases. Orthogonal projections. Orthogonal complement.  5.1 
3/233/27  CauchySchwarz inequality, triangle inequality. GramSchmidt orthogonalization and QRfactorization.Orthogonal transformations and orthogonal matrices.  5.25.3, 5.5 
3/31  Review for Midterm II.  4.14.3, 5.15.3, 5.5 
Thursday 4/2  Midterm II  4.14.3, 5.15.3, 5.5 
4/64/10  Spring recess  
4/14, 4/16  Determinants and their geometrical interpretation. Properties of determinants.  6.16.3 
4/21, 4/23  Eigenvalues and eigenvectors. Eigenspaces.  7.17.3 
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 12:001:30 in P131 (Math Tower) 
Extra review for Final  
Tuesday 5/19 11:00am1:30pm 
Final exam 