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Vjeko2 - Mathematics 33A Second Midterm November 6 2009...

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Mathematics 33A, Second Midterm, November 6, 2009. Calculators, books, or notes of any kind are not allowed on this exam. Do not use any paper other than that provided. (You may write on the back if you need more space, but indicate this clearly on the front.) There are 9 items on this exam altogether, and they all have equal value. Answer as many of them as you can. Show your work and explain your reasoning. The questions are not always arranged in order of difficulty. Look through them when you start so you get an idea of the time you’ll need. If you’re not sure what to do on an item then move onward and return to it later. Good luck. Family Name: Given names: Discussion section: UID#: Email address: Signature: Total: out of 45 points
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Question 1. (5 points) Find a basis for the plane 2 x 1 - x 2 + x 3 = 0 in R 3 . Question 2. (5 points) Find k so that the matrices 1 2 0 1 0 - 2 1 1 - 1 and 3 1 0 1 - 1 - 4 2 0 k have the same image.
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