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Appendix B Exercises
0.1 Sets
0.2 Functions
0.4 Logic
0.6 Complex numbers
0.7 Polynomials
1.1 Systems of linear equations
Exercise 9 Not all arithmetic operations preserve solutions
1.2 Gaussian elimination
1.3 Solving linear systems
2.1 Matrix arithmetic
2.2 Matrix algebra
2.3 Invertible matrices
2.4 The invertibility theorem
2.5 The determinant
3.1 Real vector spaces
3.2 Linear transformations
3.3 Subspaces
3.4 Null space and image
3.5 Span and linear independence
Exercise 21 Linear transformations, span, and independence
3.6 Bases
3.7 Dimension
3.8 Rank-nullity theorem and fundamental spaces
4.1 Coordinate vectors
4.2 Matrix representations of linear transformations
4.3 Change of basis
4.4 Eigenvectors and eigenvalues
4.5 Diagonalization
5.1 Inner product spaces
5.2 Orthogonal bases
5.3 Orthogonal projection
5.4 The spectral theorem
