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Answers to your questions 02/22/10: Administrative questions 1. Will. 2. Are there going to be proofs on the final exam? There will be easy proofs, like the ones in the quiz. 3. Suggestion regarding grading scale: If total grade including final is greater than the final grade, then use total grade for the class grade. If grade on the final is greater than total grade for entire course including the final, then use final grade for class grade. Thanks for the suggestion. I usually use the second one if the grade of the class need to be curved. 4. More examples similar to test/homework problems If time permitted. Questions on general topics 5. What does it mean for a matrix to be invertible? A matrix is invertible if it is square and Ax=0 implies x=0. Or its determinant is nonzero. 6. When can you use proof by contradiction? Under what conditions? Usually we use contradiction when the result is not easy to derive, whereas the opposite is easy to use. For example, to prove A is not B, to prove A is unique. In those cases, we suppose the opposite of the conclusion and try to get contradictions. Please write your name on the question sheet, so I can count the number of your questions for extra credits. 7. So beta prime is any basis that is not the standard ordered basis. It is a symbol to represent any basis. It can be the standard ordered basis, depending how it is defined in a specific problem. 8. Can linear algebra be used to represent circles or ellipses? It seems that the way vectors are defined it couldn’t, but the change of coordinate example given uses circles and ellipses in calculus. How would you make a curved vector? I will try to answer this question. Vectors are used to represent points on plane. Equations or

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