Test

OLLSCOIL NA hEIREANN, GAILLIMH NATIONAL UNIVERSITY OF IRELAND, GALWAY SUMMER EXAMINATIONS, 2009 FIRST utilize science & INFORMATION TECHNOLOGY EXAMINATION MATHEMATICS [MA150] MA153 | ALGEBRA professor D. Armitage Professor T. Hurley Dr. G. Ellis Dr. G. Pfeier Time allowed: iii hours. Answer sextuplet questions. 1. (a) A small dairy pretends triplet cheeses: mild, standard and mature. The pursuit table amount of moneymarizes the amount of energy, milk and drive used to produce one box of each of the terce cheeses to shrinkher with the amount of these resources usable per day. Resource Mild Standard Mature day-to-day accessible Energy 2 kWh 3 kWh 2 kWh 100 kWh take a shit out 4 L 4 L 3 L 150 L Labour 3 h 4 h 6 h 170 h Solve a schema of linear equations to determine the return gures that would ensure all resources be used. (b) Give one assess of t for which the system x + 2y = ty 2x + y = tx has innitely some solutions. (Hint: It might help to rearrange the equa- tions.) p.t.o. 2.

Let 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 then 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) go a ground substance E much(prenominal) that EA is the result of replacing the rst wrangling of A by the sum of the rst and third rows of A. 3. (a) Calculate the determinant of the ground substance A := 0 B@ 1 2 3 2 3 + t 10 2 4 t + 4 1 CA and determine all value of t fo r which A is NOT invertible. (b) Let f(t) b! e 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 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 ease up the form p + v + w...If you want to get a full essay, order it on our website: OrderCustomPaper.com

If you want to get a full essay, visit our page: write my paper