253midterm2solutions

# Linear Algebra with Applications (3rd Edition)

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ma253 , Fall 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 first two sections. Most people did ok in the problems as well. I’ve noted below a few glitches that I saw. The first 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 The nonsense choice is B . 2. Sigmund asked Brünnhilde to help him find of the subspace. a. a basis b. the dimension c. a spanning set d. the kernel The nonsense choice is D . 3. Fafner proved that { v 1 , v 2 , . . ., v p } was . The nonsense choice is C . 4. Woglinde explained that the matrix was . The nonsense choice is 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 . The nonsense choice is B . 6. Gutrune found of the linear transformation. a. the matrix b. a basis c. the rank d. the kernel The nonsense choice is B . Mark each statement of the following statesments true or false. No explanation is required, but be careful of trick questions. Each of these questions is worth 3 points . 7. If A is a 4 × 4 matrix and the rank of A is 4 , then the nullity of A is 0 .
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