sol_test2 - 1 Solutions to Test 2 - MAT1332 A- Fall 2009 1....

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Unformatted text preview: 1 Solutions to Test 2 - MAT1332 A- Fall 2009 1. [1.5 mark each] Let A = 1 2 3 1 , B = 1- 1 2 4 , and C = " 1 1 4 3 1- 2 # . Evaluate each one of the following matrices if it is defined. If an expression is undefined, explain why. (a) AB (b) BA (c) 2 A + C t where C t is the transpose of C Solution: (a) AB is undefined because number of columns in A = 3 6 = 2 = number of rows in B (b) BA = 1- 1 2 4 1 0 2 0 3 1 = 1- 3 1 2 12 8 (c) 2 A + C t = 2 1 0 2 0 3 1 + 1 1 4 3 1- 2 t = 2 0 4 0 6 2 + 1 4 1 1 3- 2 = 3 4 5 1 9 0 2. [2 marks each] Let z 1 = 1- i and z 2 = 3 + 2 i . Write: (a) iz 1 + z- 1 2 as a + bi where a and b are real numbers (b) z 1 in polar coordinates, that is, ( r cos ,r sin ) or re i Solution: (a) iz 1 + z- 1 2 = iz 1 + z 2 | z 2 | 2 = i (1- i )+ 3- 2 i 9 + 4 = i +1+ 3- 2 i 13 = 16 13 + 11 13 i (b) | z 1 | = p 1 2 + (- 1) 2 = 2 = 2 - 4 = 7 4 Thus z 1 = 2 e 7 i/ 4 or 2cos 7 4 , 2sin 7 4 ....
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sol_test2 - 1 Solutions to Test 2 - MAT1332 A- Fall 2009 1....

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