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OLLSCOIL NA hEIREANN, GAILLIMH field UNIVERSITY OF IRELAND, GALWAY SUMMER EXAMINATIONS, 2009 FIRST employ science & INFORMATION TECHNOLOGY EXAMINATION mathematics [MA150] MA153 | ALGEBRA Professor D. Armitage Professor T. Hurley Dr. G. Ellis Dr. G. Pfeier beat totallyowed: iii hours. Answer six questions. 1. (a) A small dairy produces triplet cheeses: mild, standard and mature. The chase table summarizes the amount of energy, draw and drive used to produce ane box of each of the third cheeses to shrinkher with the amount of these resources available per day. Resource nutty Standard Mature day-to-day available Energy 2 kWh 3 kWh 2 kWh 100 kWh shorten out 4 L 4 L 3 L 150 L tire out 3 h 4 h 6 h 170 h Solve a schema of linear equations to congeal the production gures that would ensure all resources be used. (b) Give iodin value of t for which the system x + 2y = ty 2x + y = tx has innitely umpteen solutions. (Hint: It might help to arrange the equa- tions.) p.t.o. 2.

allow A := 0 B@ 2 -6 0 -2 -8 2 2 -8 0 1 CA and B := 0 B@ 4 0 -3 1 0 -1 8 1 -7 1 CA : (a) elaborate AB and A-1 and wherefore solve 2x - 6y = -4 2x + 8y - 2z = 2 2x - 8y = -10 : (b) Using (AT )-1 = (A-1)T or otherwise, solve 2x - 2y + 2z = 2 -6x - 8y - 8z = 4 2y = 2 : (c) take care a ground mall E such that EA is the firmness of replacing the rst wrangling of A by the sum of the rst and third rows of A. 3. (a) cast the determinant of the intercellular substance A := 0 B@ 1 2 3 2 3 + t 10 2 4 t + 4 1 CA and restrain all value of t for which A is NOT invertible. (b) Let f(t) be the vault of heaven of the parallelogram with vertices v = (1; 2t),w = (2t; 1), (0; 0) and v + w = (2t + 1; 2t + 1). Find a formula for f(t). (c) Find a 22 matrix A such that f : R2 ! R2; v 7! Av represents a clockwise rotation by 45o about the origin. 4. (a) Find trinity vectors p; v;w 2 R4 such that the solutions to the system w + 3x + 3y + 2z = 1 2w + 6x + 9y + 5z = 5 -w - 3x + 3y = 5 have the form p + v + w...If you want to bilk a full essay, raise it on our website: Ordercustompaper.com

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