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• Can someone explain why (yx) -> (y+12x) is not a linear transformation and why (yx) -> (3y-x) is linear transformation?thank you
1. (Original post by alesha98)
• Can someone explain why (yx) -> (y+12x) is not a linear transformation and why (yx) -> (3y-x) is linear transformation?thank you
When is something a linear transformation?
2. (Original post by alesha98)
• Can someone explain why (yx) -> (y+12x) is not a linear transformation and why (yx) -> (3y-x) is linear transformation?thank you
Does the first one satisfy the property that ?
3. (Original post by Zacken)
Does the first one satisfy the property that ?
Am i on the right line?
For x:
T(kx) = Tk(x)
1(1x) = 1(2)(x)
(x) = 2(x)
4. (Original post by alesha98)
Am i on the right line?
For x:
T(kx) = Tk(x)
1(1x) = 1(2)(x)
(x) = 2(x)
Yes, so the 'x' component works.

What about the "y+1" bit? Does T(ay) = aT(y)?
5. (Original post by Zacken)
Yes, so the 'x' component works.

What about the "y+1" bit? Does T(ay) = aT(y)?
T(ky) = Tk(y)
(y) = (y+1)
In this case, i cant move out +1 from the bracket , so it doesnt satisfy?
6. (Original post by alesha98)
T(ky) = Tk(y)
(y) = (y+1)
In this case, i cant move out +1 from the bracket , so it doesnt satisfy?
pretty much
7. (Original post by Zacken)
pretty much
so when i am doing this kind of questions, i need to solve x and y separately?
Can u show me a working example?
8. (Original post by alesha98)
so when i am doing this kind of questions, i need to solve x and y separately?
Can u show me a working example?
Uh, you should just be able to spot whether they're a linear transform or not? not sure what you want
9. (Original post by Zacken)
Uh, you should just be able to spot whether they're a linear transform or not? not sure what you want
ah ok, so i dont need to prove it.
for linear transformation, it cant be
1. ie (x,y) -> (xy,y). So no xy element in the transformation
2. ie (x,y)->(x+1,y). So no constant in the transformation?

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