hwB14 - R ([ v (1) v (1) ], since b 6 = 3. Using the fact...

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ENEE 241 02* HOMEWORK ASSIGNMENT 14 Due Wed 03/05 Solve by hand without using calculator matrix functions. Show all intermediate steps. Consider the three-dimensional vectors v (1) = [1 - 2 2 4] T and v (2) = [4 2 2 1] T . (i) (4 pts.) Compute k v (1) k and k v (2) k . Show that the two vectors are orthogonal. (ii) (6 pts.) Let a = [3 - 3 2 3] T . Determine the projections f (1) and f (2) of a onto v (1) and v (2) , respectively. Also determine the angles formed between a and each of v (1) and v (2) . (iii) (5 pts.) Determine the only value of b such that the vector [3 - 3 2 b ] T is a point on the plane R ([ v (1) v (2) ]), i.e., it can be written as a linear combination of v (1) and v (2) . (iv) (5 pts.) The vector a defined in (ii) above does not lie in
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Unformatted text preview: R ([ v (1) v (1) ], since b 6 = 3. Using the fact that v (1) and v (2) are orthogonal, determine the projection of a onto the plane R ([ v (1) v (2) ]). Solved Example S 14.1 ( P 2.24 in textbook). Consider the four-dimensional vectors a = [-1 7 2 4 ] T and b = [ 3 0-1-5 ] T . (i) Compute k a k , k b k and k b-a k . (ii) Compute the angle between a and b (where 0 ). (iii) Let f be the projection of b on a , and g be the projection of a on b . Express f and g as a and b , respectively ( and are scalars). (iv) Verify that b-f a and a-g b ....
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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