11test1 - Mathematical Economics Exam#1 You have until 2:50...

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Mathematical Economics Exam #1, September 26, 2011 You have until 2:50 to complete this exam. Answer all four questions. Each question is worth 25 points, for a total of 100 points. Good luck! 1. In R 3 , a ) Find all vectors that are perpendicular to x 1 = 1 1 1 and x 2 = 2 0 1 . b ) Do the vectors described in part (a) form a vector subspace of R 3 ? Justify your answer. 2. Consider the linear system w + x + y + z = 1 w - x + y + z = 1 2 w - 3 x + 2 y + 2 z = 2 . a ) What is the rank of the matrix of coefficients? b ) Does this system have any solutions? c ) If the system has one or more solutions, describe them. Is the solution unique?
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