22Apracticemidterm2

22Apracticemidterm2 - independence. ..) Check the class FAQ...

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About the Midterm Here are some things you might want to study for the second midterm. The midterm will focus on the topics covered in class since the first midterm (i.e., it won’t be cumulative), but of course, you will still be expected to know concepts from the first part of the class that are applicable. LU decomposition (how to find L and U , how to solve Ax = b using L and U , relation to elementary matrices. ..) Elementary matrices (know the three different kinds, E i j ,R i ( λ ) ,S i j ( λ , what they are, what they do, how they relate to row reduction, how they relate to determinants and inverses. ..) Inverses (how to find using row operations, Cramer’s Rule, what a cofactor is, what an adjoint is, how to use to solve systems of equations, how the determinant is involved, conditions for invertibility. ..) Determinants (how to find a determinant (there are two ways), lots of theorems about determinants, permutations. ..) Subspaces, spanning sets, linear independence, basis (mostly know defini- tions, be able to write down the span of a set of vectors, check for linear
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Unformatted text preview: independence. ..) Check the class FAQ for some more information on a few of these topics. Now, for a few sample problems: Find the LU decomposition of M = 1 2 3 4 5 6 3 2 1 . Use the LU decompo-sition to solve the system MX = V , where V = 3 4 5 . Suppose I use row operations to transform M = 1 2 3-1 2-3 3 2 1 into M = 9 6 3 0 4 0 1 2 3 . Find a matrix E such that EM = M . Prove that if RREF ( M ) = 1 2 3 4 5 6 0 0 0 , then M cannot have an inverse. What is the determinant of the inverse of the transpose of M = 1 0-3 2 0 0-1 8 3 1 0 2-1 0 ? 1 Is 1 2 3 in the span of S = { 3 2 1 , -4 2 3 , -2 8 8 } ? Are the vectors in S linearly independent? Prove or disprove. 2...
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This note was uploaded on 03/23/2010 for the course MAT 022A taught by Professor Pon during the Spring '10 term at UC Davis.

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22Apracticemidterm2 - independence. ..) Check the class FAQ...

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