ECON 715 Midterm: ECON715 Midterm1Fall2016solution
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Instructions: one double-sided sheet with any content is allowed, calculators are not allowed, show all the calculations, and explain your steps, if you need more space, use the back of the page, fully label all graphs. 0 1 (cid:21) , b = (cid:20) 1 0 (a) calculate the matrix product aa and bb. 3x1 (cid:0) 6x2 = d1 x1 (cid:0) 2x2 = d2. 7x1 + 5x2 + 4x3 = d3 (a) write the above system in matrix form ax = d. | {z } d (b) the above system of equations has a unique solution. True/false, circle the correct answer, and provide a proof. 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 (i. e. a is invertible). Using laplace expansion along the 3rd column (easiest, because of two zeros), the determinant is jaj = 4 (cid:1)(cid:12)(cid:12)(cid:12)(cid:12)
