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Cover image of textbook Introduction to Linear Algebra, by Gilbert Strang Introduction to Linear Algebra, by Gilbert Strang

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.

Combined Solutions

Chapter 1 - Introduction to Vectors

01-1 Vectors and Linear Combinations

01-2 Lengths and Dot Products

Chapter 2 - Solving Linear Equations

02-1 Vectors and Linear Equations

02-2 The Idea of Elimination

02-3 Elimination Using Matrices

02-4 Rules For Matrix Operations

02-5 Inverse Matrices

02-6 Elimination = Factorization A=LU

02-7 Tansposes and Permutations

Chapter 3 - Vector Spaces and Subspaces

03-1 Spaces of Vectors

03-2 The Nullspace of A

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

Chapter 4 - Orthogonality

04-1 Orthogonality of the Four Subspaces

04-2 Projections

04-3 Least Squares Approximations

04-4 Orthogonal Bases and Gram-Schmidt

Chapter 5 - Determinants

05-1 The Propeties of Determinants

05-2 Permutations and Cofactors

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

Chapter 6 - Eigenvalues and Eigenvectors

06-1 Introduction to Eigenvalues

06-2 Diagonalizing a Matrix

06-3 Applications to Differential Equations

06-4 Symmetric Matrices

06-5 Positive Definite Matrices

06-6 Similar Matrices

06-7 Singular Value Decomposition (SVD)

Chapter 7 - Linear Transformations

07-1 The Idea of a Linear Transformation

07-2 The Matrix of a Linear Transformation

07-3 Change of Basis