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Appendix C Solutions to Selected Exercises
1 Vector spaces
1.2 Properties
Exercise 1.2.2.
1.2.2.a
1.2.2.b
1.2.2.c
1.2.2.d
1.6 Linear Independence
Exercise 1.6.7.
Exercise 1.6.8.
Exercise 1.6.9.
1.7 Basis and dimension
Exercise 1.7.5.
Exercise 1.7.7.
1.7.7.a
1.7.7.b
Exercise 1.7.10.
1.7.10.a
1.7.10.b
1.7.10.c
Exercise 1.7.14.
Exercise 1.7.15.
1.8 New subspaces from old
Exercise 1.8.7.
1.8.7.a
1.8.7.b
2 Linear Transformations
2.1 Definition and examples
Exercise 2.1.11.
2.2 Kernel and Image
Exercise 2.2.10.
2.2.10.a
2.2.10.b
2.2.10.c
Exercise 2.2.17.
2.2.17.a
2.2.17.b
2.3 Isomorphisms, composition, and inverses
2.3.2 Composition and inverses
Exercise 2.3.7.
Exercise 2.3.9.
3 Orthogonality and Applications
3.1 Orthogonal sets of vectors
3.1.1 Basic definitions and properties
Exercise 3.1.5.
Exercise 3.1.6.
3.1.2 Orthogonal sets of vectors
Exercise 3.1.13.
Exercise 3.1.18.
4 Diagonalization
4.2 Diagonalization of symmetric matrices
Exercise 4.2.1.
Exercise 4.2.7.
4.4 Diagonalization of complex matrices
4.4.2 Complex matrices
Exercise 4.4.8.
Exercise 4.4.12.
5 Change of Basis
5.1 The matrix of a linear transformation
Exercise 5.1.2.
Exercise 5.1.4.
Exercise 5.1.8.
5.2 The matrix of a linear operator
Exercise 5.2.4.
5.6 Jordan Canonical Form
Exercise 5.6.7.
