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## Linear Alg&Diff Eq

by: Mrs. Preston Lehner

19

0

1

# Linear Alg&Diff Eq MATH 214

Mrs. Preston Lehner
UM
GPA 3.87

Alexandra Pettet

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COURSE
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Alexandra Pettet
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Class Notes
PAGES
1
WORDS
KARMA
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## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 214 at University of Michigan taught by Alexandra Pettet in Fall. Since its upload, it has received 19 views. For similar materials see /class/231489/math-214-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15
REVIEW FOR MIDTERM 2 MATH 214 003 MARCH 26 2009 Overview The second midterm will cover sections 33 34 41 42 43 51 52 53 54 and 62 from your textbook 4th edition As for Midterm 1 there will be several multiple choice questions some questions about de nitions and problems require both computational skill and conceptual understanding Your computations will not require a calculator Textbooks notes and calculators will not be permitted De nitions to know for general linear spaces linear independence linear combination span basis dimension linear transformation invertible transformation isomorphism kernel image orthogonal vectors orthonormal vectors orthogonal linear transformation orthogonal matrix orthogonal projection onto a linear subspace orthogonal complement of a linear subspace transpose of a matrix symmetric matrix skew symmetric matrix Same note as last time about de nitions When possible it is also helpful to associate examples with de nitions You should try to memorize de nitions word for word as well as try to understand them Note that while there many be several ways to phrase a de nition it is also the case that even a slight change of wording can make a de nition wrong Computations and concepts to be familar with nding the matrix of a linear transformation with respect to a given basis changing basiscoordinate system using a change of basis matrix given a basis applying the Gram Schmidt Process to nd an orthonormal basis computing the QR factorization of a matrix applying the method of least squares computing the determinant of a matrix using the Laplace expansion and using row reduction properties of the determinant The linear spaces you should be comfortable with are R of course Rnxm and subspaces such as the set of upper triangular matrices of Rm and Pd polynomials of degree at most at

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