Mathematical Economics Midterm #1, October 2, 2000You have until 4:45 to complete this exam. Answer all five questions. Each question is worth20 points, for a total of 100 points. Good luck!1. (Linear Systems) Consider the linear systemx+y+z= 13x+ 5y+ 10z= 61.Show that this system has solutions.How many solutions are there?Can you find asolution wherex,y, andzare all positive integers?2. (Matrices) LetAandBben×nmatrices. Show that if (A+B)2=A2+ 2AB+B2,thenAB=BA.3. (Determinant) Consider the matrixA=3-4-10Find allλso that det(A-λI) = 0.4. (Linear Systems) Demand for good 1 ise1-ap1+bp2; demand for good 2 ise2+cp1-dp2;the supply of goodiissi. Herea,b,c,d,ei, ands
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