09-01-10 - Math 54 Discussion Section Problems Mike...

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Unformatted text preview: Math 54 Discussion Section Problems Mike Hartglass September 1, 2010 You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you aren’t expected to finish everything. In fact, the answers are largely unimportant; making sure everyone in your group knows how to solve all the problems is what really matters. 1. Let A = 2- 1- 6 3 , and b = b 1 b 2 . For what values of b 1 ,b 2 does the equation A x = b have a solution? What does this mean in terms of the span of the columns of A? 2. Let A = 2- 1- 6 a . For what values of a does the equation A x = b have a solution for every vector b ? Phrased another way, for what values of a do the columns of A span R 2 ? 3. As you may (or may not) have learned at some point, there is only one polynomial of degree n that passes through a given set of n + 1 points (ie, there is only one line through any given 2 points, only one parabola through a given 3 points, etc). What you may not have learned, however, is that linearone parabola through a given 3 points, etc)....
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at University of California, Berkeley.

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