253midterm2solutions

Linear Algebra with Applications (3rd Edition)

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ma253 ,Fa l l 2007 –Midterm 2 Solutions Overall, folks did pretty well; the median grade was a very high 88 points, and only two people scored below 70. In particular, I was happy to see that folks did well on the Frst two sections. Most people did ok in the problems as well. I’ve noted below a few glitches that I saw. The Frst page was essentially right out of the homework, and the solutions have already appeared in the solutions to that assignment. So I’ll be very brief here. By the way, I should point out that all the names are those of characters in Wagner’s “ring cycle” of operas. 1. Siegfried computed the of the matrix. a. rank b. basis c. kernel d. image Thenonsensecho iceis B . 2. Sigmund asked Brünnhilde to help him ±nd of the subspace. a. a basis b. the dimension c. a spanning set d. the kernel D . 3. Fafner proved that { ~ v 1 , ~ v 2 ,..., ~ v p } was . a. a spanning set b. linearly independent c. an isomorphism d. a basis C . 4. Woglinde explained that the matrix was . a. diagonal b. invertible c. in row-reduced echelon form d. a basis D . The world will change. It will probably change for the better. It won’t seem better to me. – J. B. Priestley
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5. Fricka discovered that the linear space was . a. fnite-dimensional b. invertible c. isomorphic to R 4 d. the span o± { v 1 ,v 3 5 } Thenonsensecho iceis B . 6. Gutrune ±ound o± the linear trans±ormation. a. the matrix b. a basis c. the rank d. the kernel B . Mark each statement o± the ±ollowing statesments true or ±alse. No explanation is required, but be care±ul o± trick questions. Each o± these questions is worth 3 points . 7. A is a 4 × 4 matrix and the rank o± A is 4 , then the nullity o± A is 0 . Tr ue , by the rank-and-nullity theorem. 8. The set { 1 + t, 1 + t 2 ,2t } is a basis o± P 2 .
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This homework help was uploaded on 01/23/2008 for the course MATH 253 taught by Professor Ghitza during the Fall '07 term at Colby.

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253midterm2solutions - ma253 Fall 2007 Midterm 2 Solutions...

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