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Exercise 3 6 1 In this exercise you will explore the ideas of orthogonal vectors...

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Basic Math

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Exercise 3 6 1 In this exercise you will explore the ideas of orthogonal vectors orthogonal matrices and why these ideas are useful a Plot the vectors v 2 1 b Compute v v and 22 The fact that you get an answer of 1 for both is due to the length of the vectors being equal to 1 Now compute v v2 and v2 v1 The fact that you get an answer of 0 for both of these answers is due to the fact that these two vectors are perpendicular or orthogonal to one another c Now consider the matrix A v v2 2 11 whose columns are v and v respectively and the matrix AT V A AT and AT A What does this tell you in terms of inverse matrices V 2 1 in the zy plane 1 2 11 whose rows are v and v2 transposed i e turned sideways respectively Compute d What do you think is the general fact one can say about how to construct these nice orthogonal matrices like A in general How would you go about it in words don t actually come up with an example for a 3 x 3 matrix

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