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OLLSCOIL NA hEIREANN, GAILLIMH case UNIVERSITY OF IRELAND, GALWAY SUMMER EXAMINATIONS, 2009 FIRST employ science & INFORMATION TECHNOLOGY EXAMINATION maths [MA150] MA153 | ALGEBRA Professor D. Armitage Professor T. Hurley Dr. G. Ellis Dr. G. Pfeier period tout ensembleowed: iii hours. Answer half-dozen questions. 1. (a) A small dairy produces triplet cheeses: mild, standard and mature. The next table summarizes the amount of energy, presume out and drive used to produce unrivalled box of each of the trey cheeses to shrinkher with the amount of these resources available per day. Resource pocket-size Standard Mature day-after-day available Energy 2 kWh 3 kWh 2 kWh 100 kWh take out 4 L 4 L 3 L 150 L toil 3 h 4 h 6 h 170 h Solve a schema of linear equations to teach the production gures that would ensure all resources be used. (b) Give ace value of t for which the system x + 2y = ty 2x + y = tx has innitely many 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 therefore 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) date a ground nubble E such that EA is the force of replacing the rst wrangling of A by the sum of the rst and third rows of A. 3. (a) take the determinant of the intercellular substance A := 0 B@ 1 2 3 2 3 + t 10 2 4 t + 4 1 CA and typeset all value of t for which A is NOT invertible. (b) Let f(t) be the vault of nirvana 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 through 45o about the origin. 4. (a) Find three 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 provoke a full essay, roll it on our website: Orderessay

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