- #36
Myr73
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oh ok, so how would I write out when v does not equal zero,that the range of T is the plane that is orthogonal to v
What equation? If you mean the definition of T, that's not a statement about a vector called u. It's a statement about all vectors.Myr73 said:2-I do not know u in this equation,
Just some advice about the notation: Don't type U when you mean u. These are two different symbols, so they don't automatically represent the same thing.Myr73 said:And that T(U)= v×u={v2u3-v3u2,v3u1-v1u3,v1u2-v2u1}
It looks like you ignored the formula that tells you what [T] is, and instead calculated T(u) for an arbitrary u.Myr73 said:[T]=[T(e1)|T(e2)|T(e3)].
From the first formula, I found it to be ( 0,-u3,u2). However I do not think it is correct.
You posted the formula ##[T]=[Te_1|Te_2|Te_3]##, and I explained what it means. Why not use that?Myr73 said:"If X=Y, it's convenient to choose B=A, and to speak of the matrix representation of T with respect to A instead of with respect to (A,A), or (A,B). The formula for Tij can now be written as
Tij=(Tej)i=(Tei),(Tej)"
I guess what I did not understand is how to refer it to the matrix of the transformation T(u)=v×u.
Yes, because ##e_1=(1,0,0)##.Myr73 said:But by [T1]= (e1)×(e1)=0, would this be like doing the cross product of (1,0,0) and (1,0,0). ?
It looks like you're just guessing now. You have to use the definition of T.Myr73 said:[T2]= (e2)×(e2)=0, [T3]=(e3)×(e3)=0.
Why would you think that?Myr73 said:I am not sure, but i thought
T2=(e2)x(e2)
Yes, but that's not a reason to think that the second column is ##e_2\times e_2##. That's why I said that you seem to be guessing now.Myr73 said:because you said that [T1]=e1xe1