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Unformatted text preview: MAS 3105 June 11, 2009 Quiz 6 and Key Prof. S. Hudson 1a) Let P 1 = (1 , 2 , 2), P 2 = (0 , 1 , 2) and P 3 = (0 , 1 , 1). Find a nonzero normal vector N , for the plane containing these three points in R 3 . [You may be able to solve this without GE - if so, be sure to show enough work, or explain your reasoning]. 1b) Find an equation for this plane. 2) Give an explicit example of a matrix B 6 = A which is similar to A : A = 1 1 0 1 3) Choose ONE and circle it. Answer on the back. a) State and prove the Fundamental Subspace Theorem (5.2.1). b) Prove (from the definition) that if A is similar to B and B is similar to C , then A is similar to C . Bonus [5pts]: Give an example of an inconsistent system which has more than one Least Squares solution, and find at least two solutions. Remarks and Answers: The average grade was approx 38 out of 60, a bit low, but not too bad. Problem 1a) was similar to a moderately-difficult HW problem 5.2.5; problem 2 should be pretty easy. The scale for this quiz is the same as for Q4.should be pretty easy....
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- Spring '09
- Want, Linear least squares, nonzero normal vector