# ass5 - 2 4 Brand 2 1 1 3 Brand 3 1 1(a Find all combination...

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Professor Robert Smith?, University of Ottawa, MAT 1332, Winter 2011 Assignment 5, due Wednesday March 16, 8:30am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Student Number DGD section By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Student Name 1. For the system of linear equations x + 3 y + 9 z = 3 2 x + 7 y + 23 z = 2 x + ay + a 2 z = a (a) determine the values of a for which the system has (i) no solution, (ii) inﬁnitely many solutions, (iii) a unique solution. (b) In case (ii) above describe all solutions. (c) If a = 1 ﬁnd the inverse of the matrix A = 1 3 9 2 7 23 1 a a 2 2. Your doctor has asked you to take 5 units of vitamin A, 13 units of vitamin B and 23 units of vitamin C every day. There are three brands available in your local pharmacy which contain the following units of vitamins A, B, C as indicated. vitamin A vitamin B vitamin C Brand 1 1

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Unformatted text preview: 2 4 Brand 2 1 1 3 Brand 3 1 1 (a) Find all combination of pills that provide you with the exact daily requirement (no partial pills!). (b) If brands 1, 2, and 3 cost \$0.60, \$0.40, and \$1.00 per pill respectively, ﬁnd the least expensive treatment and its cost. 1 3. Given the following matrices and vectors A = 1-7-9 6 8 4 4 , B = 3-7 6 4 1 , u = 1 2 3 , v = 1 7 / 4 , w = 1 / 2 3 / 4 . Compute the following if possible. If not possible, explain in one sentence why. (a) 3 v + 2 B T w . (b) wv T (c) v T w (d) A T B + 2 v T w (e) AB (f) B u (g) BA (h) A 2 4. Determine the matrix A such that: ± 3 A T-² 1 3-2-4 5 1 ³ ´ T = -4 3 2 4-2 6 + 3 ² 7-5 4 9 12 3 ³ T . 5. Draw the following complex numbers in the plane :-1 + 2 i,-3 + 2 i, (-1 + i )(1 + 2 i ) , (2 + i ) 2 , (1 + i )-1 . 2...
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ass5 - 2 4 Brand 2 1 1 3 Brand 3 1 1(a Find all combination...

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