Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 6 - Orthogonality and Least Squares - 6.1 Exercises - Page 338: 17

Answer

Since 0 = 0, the vectors are orthogonal.

Work Step by Step

Note: Vectors can be rewritten using <>, so u = <3, 2, -5, 0> v = A vector is orthogonal if the dot product of the two vectors is 0, so we have to check if uāˆ™v = 0. The dot product can be formed by multiplying the first components of the vector together, multiplying the second components of the vector together, multiplying the third components of the vector together, multiplying the fourth components of the vector together, and adding all the products together. 1. Multiply the first components: 3 * -4 = -12 2. Multiply the second components: 2 * 1 = 2 3. Multiply the third components: -5 * -2 = 10 4. Multiply the fourth components: 0 * 6 = 0 5. Add the products together: -12 + 2 + 10 + 0 = 0 Since 0 = 0, the vectors are orthogonal.
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