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HW1 - Math 3013 Homework Set 1 Problems from 1.1(pg 15 17...

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Math 3013 Homework Set 1 Problems from § 1.1 (pg. 15 - 17 of text): 1,9,31,35 Problems from § 1.2 (pg. 31 - 33 of text): 1,3,22,23,25,27,33 Problems from § 1.3 (pg. 46 - 48 of text): 1,3,7,9,11,13,14,19,21 1. (Problem 1.1.1 and 1.1.3 in text). Let v = [2 , - 1] and w = [ - 2 , - 3]. Compute v + w , v - w and then draw coordinate axes and sketch, using your answers the vectors v , w , v + w , and v - w . (a) v = [2 , - 1], w = [ - 3 , - 2]. (b) v = i + 3 j + 2 k , i + 3 j + 4 k , where i = [1 , 0 , 0], j = [0 , 1 , 0], k = [0 , 0 , 1] are the standard basis vectors of R 3 . 2. (Problem 1.1.9 in text). Let u = [1 , 2 , 1 , 0], v = [ - 2 , 0 , 1 , 6] and w = [3 , - 5 , 1 , - 2]. Compute u - 2 v +4 w . 3. (Problem 1.1.31 in text). Find the vector which, when translated, represents geometrically an arrow reaching from the point ( - 1 , 3) to the point (4 , 2) in R 2 . 4. (Problems 1.2.1 and 1.2.3 in text). Let u = [ - 1 , 3 , 4] and v = [2 , 1 , - 1]. Compute - u and v + u . 5. (Problem 1.2.22 in text). Compute the angle between [1 , - 1 , 2 , 3 , 0 , 4] and [7 , 0 , 1 , 3 , 2 , 4] in R 6 . 6. (Problem 1.2.23 in text) Prove that (2 , 0 , 4), (4 , 1 , - 1) and (6 , 7 , 7) are the vertices of a right triangle in R 3 . 7. (Problems 1.2.25 and 1.2.27 in text). Classify the vectors as parallel, perpendicular, or neither. If they are parallel, state whether they have the same or opposite directions. (a) [ - 1 , 4] and [8 , 2]. (b) [3 , 2 , 1] and [ - 9 , - 6 , - 3]. 8. (Problem 1.2.22 in text). Find the distance between the points (2
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