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FinalReview - Newberger Math 247 Spring 03 Review sheet for...

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Newberger Math 247 Spring 03 Review sheet for the Final Exam Part I This part of the final exam will be over material covered since the second midterm. It will cover Sections 4.1-4.4, 4.7, 5.1, 5.2. You will be asked to state the definitions of the following terms. Use precise language; to be safe, you may want to use the defi- nitions straight from the text. 1. The coordinates of a vector relative to a basis. (See p246.) 2. Eigenvalue and eigenvector. Other vocabulary that you should be familiar with: 1. Subspace of a vector space. 2. Null space and column space of a matrix. 3. Basis. 4. The vector space P n . 5. Change of coordinates matrix. 6. Eigenspace. 7. Characteristic equation. From Sections 4.1-4.4 and 4.7: 1. You will be asked to determine whether or not a given set is a subspace of a vector space, and to show that your answer is correct. To show that a given set is not a subspace, you must either prove that the zero vector is not in the given set or give a specific numeric example for which one of the other properties of a subspace fails.
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