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Unformatted text preview: Math 235 Final Review Problems 1. Know all definitions and Theorems! 2. What is the definition of the four fundamental subspaces? 3. Linear Mappings a) What is the RankNullity theorem? b) How do you find the rank and/or nullity of a linear mapping? c) How do you find the matrix of a linear operator with respect to a basis B ? How do you find the matrix of a linear mapping L : V → W with respect to a basis B for V and a basis C for W . 4. Isomorphisms a) What is the definition of an isomorphism? b) What are some theorems about isomorphisms? c) What is a general method for finding an isomorphism? Know how to prove a mapping is an isomorphism. 5. Inner Products a) What is the definition of the inner product? Real? Complex? b) Let A = 6 2 2 3 . Is < ~x,~ y > = ~x T A~ y an inner product for R 2 ? c) What is the definition of an orthogonal matrix? What are some properties of orthog onal matrices?...
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This note was uploaded on 09/30/2011 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.
 Spring '08
 CELMIN
 Math

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