Linear Algebra: Proving Linear Transformation | Mathematics | Page 1

tidal stormBOT Jul 21, 2023, 4:44 PM

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long phoenix Jul 21, 2023, 4:47 PM

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What do you know about the dimensions of every space mentioned here?

drowsy thunder Jul 21, 2023, 4:48 PM

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nothing, i think it’s arbitrary?

long phoenix Jul 21, 2023, 4:51 PM

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What is the dimension of K? What is the dimension of R?

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those are not arbitrary.

drowsy thunder Jul 21, 2023, 4:52 PM

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ohh sorry

long phoenix Jul 21, 2023, 4:54 PM

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R^3 has dimension 3. That means that f will have 3 dimensions to work with.

drowsy thunder Jul 21, 2023, 4:54 PM

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here is my answer tho i’m not sure if it’s correct.

long phoenix Jul 21, 2023, 4:55 PM

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but f is being forced to kill a bunch of the vectors in its domain.

drowsy thunder Jul 21, 2023, 4:55 PM

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long phoenix Jul 21, 2023, 4:57 PM

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This looks good. I'm not finished reading it, but I just wanted to say that in the line where you say f(x_1) = (1,1) and f(x_2)=(1,1), you don't actually need those to equal (1,1), they only need to be in the span of (1,1).

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You also don't need x_1 and x_2

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Oh, wait, you have the wrong conclusion.

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dim(K)=2, and dim(R)=1

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And remember that dim(ker(f)) + dim(im(f)) = dim(dom(f))

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2+1=3 is true, so you should be able to find f.

drowsy thunder Jul 21, 2023, 5:00 PM

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so there is linear transformation?

long phoenix Jul 21, 2023, 5:01 PM

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Yes.

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where you found that b=-a and c=-a, that was really good, but you should also find out something about d,e,f

drowsy thunder Jul 21, 2023, 5:02 PM

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okay okay i’ll try to answer it again, thank you for your help really 🙂 🫡

long phoenix Jul 21, 2023, 5:03 PM

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You're welcome. It's always nice to help someone who has thought about the question and tried something and shows what they have.

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This is a good start. I'm sure you'll have it soon. Feel free to post what you get here to check it.

#Linear Algebra: Proving Linear Transformation