Test

OLLSCOIL NA hEIREANN, GAILLIMH NATIONAL UNIVERSITY OF IRELAND, GALWAY SUMMER EXAMINATIONS, 2009 FIRST apply science & INFORMATION TECHNOLOGY EXAMINATION MATHEMATICS [MA150] MA153 | ALGEBRA prof D. Armitage Professor T. Hurley Dr. G. Ellis Dr. G. Pfeier Time allowed: iii hours. Answer half-dozen questions. 1. (a) A small dairy bring forths triplet cheeses: mild, standard and mature. The spare-time activity table nitty-grittymarizes 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 getable per day. Resource Mild Standard Mature day-to-day ready(prenominal) Energy 2 kWh 3 kWh 2 kWh 100 kWh germinate 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 drudgery gures that would ensure all resources be used. (b) Give one economic value of t for which the system x + 2y = ty 2x + y = tx has innitely many solutio ns. (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) bring 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 matrix A := 0 B@ 1 2 3 2 3 + t 10 2 4 t + 4 1 CA and determi ne all value of t for which A is NOT inverti! ble. (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 much(prenominal) 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 arrive at the form p + v + w...If you want to get a full essay, order it on our website: BestEssayCheap.com

If you want to get a full essay, visit our page: cheap essay