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Appendix G Video examples and figures
0.5 Proof techniques
Figure 0.5.9 Mathematical induction as ladder of propositions
1.1 Systems of linear equations
Figure 1.1.8 Using Sage to visualize
\(\mathcal{P}\colon ax+by+cz=d\) via normal vector
\(\boldn=(a,b,c)\)
1.3 Solving linear systems
Figure 1.3.9 Decision tree for number of solutions to a system
2.1 Matrix arithmetic
2.2 Matrix algebra
2.4 The invertibility theorem
2.5 The determinant
3.2 Linear transformations
3.3 Subspaces
Figure 3.3.5 Video: deciding if
\(W\subseteq V\) is a subspace
Figure 3.3.6 Video: deciding if
\(W\subseteq V\) is a subspace
3.4 Null space and image
3.5 Span and linear independence
3.6 Bases
3.7 Dimension
3.8 Rank-nullity theorem and fundamental spaces
4.3 Orthogonal projection
5.1 Coordinate vectors
5.2 Matrix representations of linear transformations
5.3 Change of basis
5.4 Eigenvectors and eigenvalues
5.5 Diagonalization
5.6 The spectral theorem
