Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

 Math 2360 Linear Algebra Fall 2009 Leon, Steven J Linear Algebra Pearson

Review Exam III
 Section Content Suggested Problems Section 4.1 Examples Matrix Multiplication Properties L(0V) = 0W L(-x) = -L(x) Linear combinations Kernel of L Image of a Subspace under L Range of L Theorem 4.1.1 1, 4, 5, 6, 7, 9, 11, 17, 19 Section 4.2 Theorem 4.2.1 Matrix representation of Linear Transformation from Rn to Rm Theorem 4.2.2 Matrix representation of Linear Transformation from V to W Theorem 4.3.3 Construction of Matrix A for case of V = Rn and W = Rm in Theorem 4.2.2 Corollary Above construction via row equivalent transformation of an augmented matrix 1, 2, 3, 4, 6, 14, 18 Section 4.3 Linear Operator Theorem 4.3.1 Similarity 1, 3, 4, 5 Section 5.1 Scalar product of vectors in Rn Length of a vector in in Rn Distance between two vectors in in Rn Angle between two vectors in Rn Cauchy-Schwarz Inequality Definition of orthogonality for vectors in Rn Projections Vector projection of x onto y Scalar rojection of x onto y 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, Section 5.2 Orthogonal subspaces Orthogonal complement of a subspace Theorem 5.2.1 Fundamental Subspaces Theorem Direct sum of subspaces Theorem 5.2.3 1, 2, 4, 5, Section 5.3 Least Square Problem for Ax = b Theorem 5.3.1 Normal Equations for Least Squares Problem Theorem 5.3.2 Least squares soluton for matrix A with rank n 1a, 1b, 2

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