The downloadable files below, in PDF format, contain answers to selected exercises from the 3rd edition, chapters 1 - 7. To download a PDF file to your computer, click on a chapter heading below, and then save the file when prompted. A combined file (16 MB) of all the individual files is also available for download.

01-1 Vectors and Linear Combinations

02-1 Vectors and Linear Equations

02-3 Elimination Using Matrices

02-4 Rules For Matrix Operations

02-6 Elimination = Factorization A=LU

02-7 Tansposes and Permutations

03-3 The Rank and Row Reduced Form

03-4 The Complete Solution To AX=B

03-5 Independence, Basis and Dimension

03-6 Dimensions ofthe Four Subspaces

04-1 Orthogonality of the Four Subspaces

04-3 Least Squares Approximations

04-4 Orthogonal Bases and Gram-Schmidt

05-1 The Propeties of Determinants

05-2 Permutations and Cofactors

05-3 Cramer's Rule, Inverses, and Volumes

06-1 Introduction to Eigenvalues

06-3 Applications to Differential Equations

06-5 Positive Definite Matrices

06-7 Singular Value Decomposition (SVD)

07-1 The Idea of a Linear Transformation

07-2 The Matrix of a Linear Transformation