Lect1-01-web

Lect1-01-web - MATH 304, Fall 2011 Linear Algebra Course...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 304, Fall 2011 Linear Algebra Course outline Part I ( 3 weeks): Elementary linear algebra Systems of linear equations Gaussian elimination process, Gauss-Jordan reduction Matrix algebra Determinants and their properties Part II ( 4.5 weeks): Abstract linear algebra Vector spaces Linear independence of vectors Basis of a vector space and dimension Coordinates, their dependence on change of basis Linear transformations of vector spaces Course outline Part III ( 4 weeks): Advanced linear algebra Orthogonality of vectors, least squares problems Inner product and norm The Gram-Schmidt orthogonalization process Eigenvalues and eigenvectors of matrices Diagonalization of matrices Part IV ( 2 weeks): Some topics in applied linear algebra Matrix exponentials Rotations in space Orthogonal polynomials Fourier series MATH 304 Linear Algebra Part I ( 3 weeks): Elementary linear algebra Systems of linear equations Gaussian elimination, Gauss-Jordan reduction Matrices, matrix algebra Determinants Leons book : Chapters 12 MATH 304 Linear Algebra Lecture 1: Systems of linear equations. Gaussian elimination. Linear equation The equation 2 x + 3 y = 6 is called linear because its solution set is a line in R 2 (and because the powers of x and y are 1: 2 x 1 + 3 y 1 = 6 . The equation x 2 + 3 xy + y 2 = 1 would be called quadratic etc). A solution of the equation is a pair of numbers ( , ) R 2 such that 2 + 3 = 6. For example, (3 , 0) and (0 , 2) are solutions. Alternatively, we can write the first solution as x = 3, y = 0. x y 2 x + 3 y = 6 General equation of a line: ax + by = c , where x , y are variables (called sometime unknowns) and a , b , c are constants (except for the case a = b = 0). Definition. A linear equation in n variables x 1 , x 2 , . . . , x n is an equation of the form a 1 x 1 + a 2 x 2 + + a n x n = b , where a 1 , . . . , a n R , and b R are constants....
View Full Document

This note was uploaded on 11/08/2011 for the course MATH 304 taught by Professor Hobbs during the Spring '08 term at Texas A&M.

Page1 / 35

Lect1-01-web - MATH 304, Fall 2011 Linear Algebra Course...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online