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# LINEAR ALGEBRA MATH 544

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This 2 page Class Notes was uploaded by Cassidy Grimes on Monday October 26, 2015. The Class Notes belongs to MATH 544 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/229553/math-544-university-of-south-carolina-columbia in Mathematics (M) at University of South Carolina - Columbia.

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Date Created: 10/26/15

Math 544 Exam 1 Information Exam 1 Will be based on 0 Sections 11 13 15 17 and 19 o The corresponding assigned homework problems see httpwwwmathsceduNboylanSCCoursesmathS443544html At minimum you need to understand how to do the homework problems 0 Lecture notes 824 921 Topic List not necessarily comprehensive You will need to know how to de ne vocabulary wordsphrases de ned in class 11 Matrix representation of a linear system coe icient matrix augmented matrix ele mentary row operations row equivalence 12 Solving linear systems via Gauss Jordan elimination echelon and reduced echelon forms of a matrix identifying dependent and independent variables recognizing when a system is consistent inconsistent 13 Relationship between the number of nonzero rows the number of leading 1 s and the number of columns in an augmented matrix in reduced echelon form Homogeneous linear systems The number of possible solutions to for example 1 a general linear system 2 an m X 72 system with m lt n 3 a homogeneous system 15 Matrix operations addition multiplication multiplication by scalars dot product in R 16 Properties of matrix addition multiplication and multiplication by scalars The matrix transpose and its properties What is the transpose of a product What is a symmetric matrix Also vector norm length in terms of the dot product 17 Linear combinations linear dependenceindependence determinination of whether a given set of vectors is linearly dependentindependent Nonsingular matrices remem ber only square matrices can be singular or nonsingular conditions equivalent to non singularity ofA E Matnm R 1 Am 6 has only the trivial solution m 6 2 columns of A are linearly independent 3 Vb 6 1R Am bhas a unique solution 4 A is invertible 5 A is row equivalent to the identity In 19 Matrix inverses existence of inverses see above eg A is invertible ltgt A is non singular using inverses to solve systems computing inverses by row reduction formula for inverse of 2 X 2 matrix algebraic properties of inverses eg what is the inverse of a product of two matrices Remember only square matrices can be invertible Notes 0 Only sets of vectors can be linearly dependentindependent It does not make sense to speak of matrices or systems of equations being linearly dependent independent 0 Only systems of linear equations can be consistentinconsistent It does not make sense to speak of matrices or sets of vectors as consistentinconsistent 0 Only squares matrices can be singularnon singular It does not make sense to speak of a system of equations or set of vectors as being singularnonsingular The same applies for inveltibility

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