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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Kirchhoff’s laws and their matrix interpretations
Section 4.1
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Orthogonal subspaces
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 Spring '08
 Staff
 Linear Algebra, Algebra, Linear Equations, Equations, Vectors, Matrices, Systems Of Linear Equations, Dot Product, Inverse matrix Section, elimination matrices Section, Rn Section, mxn matrix Section, nondiagonalizable matrices Section

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