- #1
haribol
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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:Rn to Rm
T(x,y)=(2x,y)
Solution from solutions manual:
T((x1,y1) + (x2,y2)) = (2(x1+x2), y1+y2) = (2x1,y1) + (2x2,y2) = T(x1,y1) + T(x2,y2)
My questions are
1. Where did the x1's and the x2's and the y1's and the y2's come from?
2. Can you please explain what's happening step by step?
[PS]--> The questions asks to use the theorem which states:
A transformation T:Rn --> Rm is linear if and only if the following relationships hold for all vectors u and v in Rn and every scalar c
a) T(u+v) = T(u) + T(v)
b)T(cu) = cT(u)
I would be very grateful if someone can explain what is going on in the following problem:
Determine whether the following T:Rn to Rm
T(x,y)=(2x,y)
Solution from solutions manual:
T((x1,y1) + (x2,y2)) = (2(x1+x2), y1+y2) = (2x1,y1) + (2x2,y2) = T(x1,y1) + T(x2,y2)
My questions are
1. Where did the x1's and the x2's and the y1's and the y2's come from?
2. Can you please explain what's happening step by step?
[PS]--> The questions asks to use the theorem which states:
A transformation T:Rn --> Rm is linear if and only if the following relationships hold for all vectors u and v in Rn and every scalar c
a) T(u+v) = T(u) + T(v)
b)T(cu) = cT(u)