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Asked Sep 23, 2019
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17) Let T be a linear transformation from R° to R, andu and v be orthogonal vectors. Which of the
following pairs of vectors must be orthogonal?
a) Tu and u
b) Tv and v
Tu and Tv
c)
d)
ru and sv (where r and s are real numbers)
e) u+v and u-v
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3 3 17) Let T be a linear transformation from R° to R, andu and v be orthogonal vectors. Which of the following pairs of vectors must be orthogonal? a) Tu and u b) Tv and v Tu and Tv c) d) ru and sv (where r and s are real numbers) e) u+v and u-v

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Expert Answer

Step 1

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(Tим)- (v.и} (if Tu v) =0 Therefore, Tu and u are orthogonal if Tu = v

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Step 2

b)

Check Tv and v are orthogonal or not.

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(Tv.v)= (u,v) (if Tv u) =0 Therefore, Tv and v are orthogonal if Tv = u

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Step 3

c)

Check Tu and Tv are orthogon...

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(Tи,Tv)-(и,v) (if Tu v and Tv = u) =0 Therefore, Tu and Tv are orthogonal if Tu = v and Tv = u

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