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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Last modified on: Monday, 10-Aug-2015 12:47:29 CDT