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Dr Arthur Rubin
Dr Arthur Rubin, Doctoral Degree
Category: Calculus and Above
Satisfied Customers: 1493
Experience:  Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers
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Prove that there is only one linear transformation, T:R^n

Customer Question

Prove that there is only one linear transformation, T:R^n --> R^m such that T(u-v) = T(u+v) for every pair of vectors u, v include R^n
Submitted: 10 months ago.
Category: Calculus and Above
Customer: replied 10 months ago.
Is there any approximate of how long the wait is for the answer to this question? -Thanks
Customer: replied 10 months ago.
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Expert:  Mr. Gregory White replied 10 months ago.

Hello, my name is Greg.

Can you provide the specifics of what you are needing for this prompt as what you have provided above does not really show what is required. The more information you can provide, the easier it will be to find an expert who is best able to support your needs.

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Expert:  Dr Arthur Rubin replied 10 months ago.

I don't see the difficulty.

If T(u-v) = T(u+v), then

T(u) - T(v) = T(u) + T(v)

T(v) + T(v) = 0

T(v) = 0

Hence the only such linear transformation is the zero map.

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