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Ma1502HW3-Spring2010

# Ma1502HW3-Spring2010 - MATH1502 Homework 3 Spring 2010 due...

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MATH1502 - Homework 3 Spring 2010 - due Tuesday April 13 Name _____________________________ Group (e.g. G1 or H1) _____________________ Student Number ____________________ Teaching Assistant ____________________ .. Question Number Points Total 100 (100=100%). Question 1 Consider the following four matrices A; B; C; D . A = 2 6 6 4 0 3 2 11 2 0 ° 1 3 4 ° 1 0 1 3 7 7 5 ; B = 2 4 6 2 3 2 ° 2 0 1 ° 1 5 3 5 ; C = ° 7 1 0 ° 2 0 ° 5 0 2 ± ; D = ° ° 1 1 7 0 1 3 ± : 1

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Which of the 16 possible products AA; AB; AC; AD; ::: make sense? Com- pute the products that do make sense. 2
Question 2 Let a; b; c be real numbers and A = ° ° 7 c a 4 ± ; B = ° ° 1 7 + c b 0 1 4 ± : (a) Compute AB: (b) For which values of a; b; and c is B = A ° 1 ? 3

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Question 3 Let ° 2 ² 0 ; ° 2 ³ and S ( ° ) = ° ° tan ° cot ° 1 1 ± : Use the formula for the inverse of a 2 by 2 matrix to compute S ( ° ) ° 1 : 4
Question 4 Consider the vectors v 1 = 2 4 3 2 1 3 5 ; v 2 = 2 4 ° 2 2 2 3 5 ; v 3 = 2 4 2 ° 2 4 3 5 : (a) Compute v i ± v j for i; j = 1 ; 2 ; 3 : (b) What are the lengths of these vectors? (c) What are the angles between the 3 pairs of vectors? Is any pair orthogo- nal?

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