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by: Pansy Cronin

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# Elementary Linear Algebra MTH 329

Marketplace > Marshall University > Mathematics (M) > MTH 329 > Elementary Linear Algebra
Pansy Cronin
Marshall
GPA 3.51

Staff

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COURSE
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KARMA
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## Popular in Mathematics (M)

This 0 page Study Guide was uploaded by Pansy Cronin on Sunday November 1, 2015. The Study Guide belongs to MTH 329 at Marshall University taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/233245/mth-329-marshall-university in Mathematics (M) at Marshall University.

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Date Created: 11/01/15
08092007 Elementary Linear Algebra MTH 329 STUDY SHEET for FINAL EXAM Friday August 10 The test will cover Ch 1 sections 11713 Ch 2 sections 21 7 24 Ch 3 sections 317 33 35 7 37 Ch 4 sections 41 7 44 46 Ch 6 section 61 The best way to prepare to the midterm is to read the book and to do the homework exercises Please take time to go over the material 1 Chapter 1 Vectors 1 Vectors in R2 R3 and Rquot 2 Vector operations addition scalar multiplication subtraction 3 Linear combination of vectors 4 The dot product length of a vector distance between two vectors angle between two vectors projection of one vector on another Triangle inequality Orthogonal vectors Lines and planes in R2 and R3 The normal and general form of the equations of lines and planes The vector and parametric form of the equations of lines and planes Distance from a point to a line Distance from a point to a plane V39 11 Chapter 2 Systems of Linear Equations A linear equation A system of linear equations The solution set for a linear system Back substitution method Consistent and inconsistent linear systems Elementary row operations Row equivalent matrices Row echelon form of a matrix Gaussian elimination Row reduced echelon form of a matrix GaussJordan elimination The rank of a matrix Homogeneous systems Spanning sets and linear independence of vectors Applications allocation of resources network analysis 9 908994 111 Chapter 3 Matrices ws www bP N 509080 Matrix operations addition scalar multiplication subtraction matrix multiplication Matrix powers transposition symmetric matrices Properties of matrix operations The inverse of a matrix invertible matrices Properties of invertible matrices Twobytwo matrices Elementary matrices Fundamental theorem of invertible matrices GaussJordan method for computing inverse Subspaces row space column space null space Basis dimension rank Linear transformations Applications Leslie matrices graphs and digraphs adjacency matrices Chapter 4 Eigenvalues and Eigenvectors Eigenvalues and eigenvectors of 2x2 matrices Determinants 3x3 matrices Minors cofactors cofactor expansion along the ith row Properties of determinants computing the determinant by reduction to row echelon form triangular matrix Cramer s rule Eigenvalues and Eigenvectors of mm matrices Similarity and Diagonalization Application power of a matrix Applications Leslie matrices linear recurrence relations V Chapter 6 Vector Spaces 1 2 3 De nition of a Vector Space Examples of vector spaces Subspaces

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