ECON 715 Midterm: ECON715 Midterm1Fall2015solution
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Instructions: one double-sided sheet with any content is allowed, calculators are not allowed, show all the calculations, if you need more space, use the back of the page, fully label all graphs. Aa = (cid:20) 6 (cid:0)10 (cid:0)5 (cid:21) (cid:0)10 (cid:0)5 (cid:21)(cid:20) 6 (cid:0)60 + 50 (cid:0)30 + 25 (cid:21) =(cid:20) 6. 4x1 + 3x2 + 6x3 = d3 (a) write the above system in matrix form ax = d. 5 (b) the above system of equations has a unique solution. True /false, circle the correct answer, and provide a proof. All we need to determine the existence of a unique solution is the determinant of: laplace expansion along the second row is easiest, because of the two zeros: A n (cid:2) n system of linear equations has a unique solution if and only if the de- terminant of the coe cient matrix jaj 6= 0. Therefore, the given system has a unique solution.
