final_review_s11

final_review_s11 - Math 235 Final Review Problems 1. Know...

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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 Rank-Nullity 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.

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final_review_s11 - Math 235 Final Review Problems 1. Know...

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