(adsbygoogle = window.adsbygoogle || []).push({}); Linear Transformations Rn-->Rm Question

I would be very grateful if someone can explain what is going on in the following problem:

Determine whether the following T:R^{n}to R^{m}

T(x,y)=(2x,y)

Solution from solutions manual:

T((x_{1},y_{1}) + (x_{2},y_{2})) = (2(x_{1}+x_{2}), y_{1}+y_{2}) = (2x_{1},y_{1}) + (2x_{2},y_{2}) = T(x_{1},y_{1}) + T(x_{2},y_{2})

My questions are

1. Where did the x_{1}'s and the x_{2}'s and the y_{1}'s and the y_{2}'s come from?

2. Can you please explain whats happening step by step?

[PS]--> The questions asks to use the theorem which states:

A transformation T:R^{n}--> R^{m}is linear if and only if the following relationships hold for all vectorsuandvin R^{n}and every scalar c

a) T(u+v) = T(u) + T(v)

b)T(cu) = cT(u)

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# Homework Help: Linear Transformations Rn->Rm Question

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