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FinalReview%20415

# FinalReview%20415 - Math 415 Topics covered by the Final...

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Math 415. Topics covered by the Final exam Section 1.1, 1.2. Vectors and linear combination Dot product Section 1.3 Matrices, matrix of coefficients Inverse matrix Section 2.1 Vector and matrix versions of systems of linear equations Section 2.2, 2.3 Elimination and elimination matrices Section 2.4, 2.5 Matrix operations Block multiplication Inverses Section 2.6 LU factorization Section 2.7 Transposes and permutation Section 3.1 Vector spaces and subspaces Col(A) Section 3.2 Null space Theorem: if n>m then there must be free variables Section 3.3 Rank and dimension of Col(A), N(A) Section 3.4. The complete solution to Ax=b (particular solution + N(A)) Section 3.5 Linear independence Basis Dimension Bases for Row(A) and Col(A) Section 3.6 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 Graphs and networks Kirchhoff’s laws and their matrix interpretations Section 4.1 Orthogonal subspaces
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FinalReview%20415 - Math 415 Topics covered by the Final...

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