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Math 415.
Topics covered by the Final exam
Section 1.1, 1.2.
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Vectors and linear combination
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Dot product
Section 1.3
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Matrices, matrix of coefficients
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Inverse matrix
Section 2.1
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Vector and matrix versions of systems of linear equations
Section 2.2, 2.3
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Elimination and elimination matrices
Section 2.4, 2.5
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Matrix operations
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Block multiplication
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Inverses
Section 2.6
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LU factorization
Section 2.7
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Transposes and permutation
Section 3.1
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Vector spaces and subspaces
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Col(A)
Section 3.2
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Null space
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Theorem: if n>m then there must be free variables
Section 3.3
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Rank and dimension of Col(A), N(A)
Section 3.4.
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The complete solution to Ax=b (particular solution + N(A))
Section 3.5
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Linear independence
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Basis
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Dimension
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Bases for Row(A) and Col(A)
Section 3.6
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Dimension of the 4 subspaces

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Theorem: dim(Col(A))+dim(N(A))=n if A is an mxn matrix
Section 8.2
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Graphs and networks
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