tutorial 6 - 7 . 1) Show that ~x W . 1 2) Find other...

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MATH1104C — Tutorial 6 1. Let ~u = 3 - 1 - 2 and ~v = 1 - 2 0 . 1) Find the distance between two vectors 2) Normalize the vector ~u . 3) Calculate the dot product. Solution: 1) 3 . 2) 3 14 - 1 14 - 2 14 3) 5. 2. Let ~u = 3 - 1 - 2 k 2 and ~v = 1 - 2 k 0 . Find k such that the two vectors are orthogonal. Solution: 2 . 5 . 3. Show that the set of vectors 1 1 1 , 1 - 1 0 , - 1 - 1 2 , is orthogonal. Is the set linearly independent? Solution: yes. 4. Let W = span - 1 2 1 , 3 1 1 , ~x = 1 4 -
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Unformatted text preview: 7 . 1) Show that ~x W . 1 2) Find other vectors in W . Solution: 1) -1 2 1 ~x = 0 , 3 1 1 ~x = 0 . 2) Let ~x = x 1 x 2 x 3 W . Then -1 2 1 ~x = 0 , 3 1 1 ~x = 0 A~x = 0 , A = "-1 2 1 3 1 1 # "-4 1 0 7 4 # . The solution of this is: x 1 = 1 / 4 x 2 ,x 3 =-7 / 4 x 2 , i.e., ~x = 1 / 4 x 2 1 4-7 . 2...
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tutorial 6 - 7 . 1) Show that ~x W . 1 2) Find other...

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