Transition Matrices: Solving X[T]X & T(v_1)=v_2

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The discussion centers on understanding the computation of the expression X[T]X and the linear transformation properties T(v_1) = v_2 and T(v_2) = av_1 + bv_2. Participants clarify that these equations are illustrative examples rather than derived from specific principles. The confusion arises from interpreting these transformations as general rules rather than specific cases. Ultimately, the consensus is that the transformations serve as examples to illustrate linear mappings.

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Artusartos
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I am a bit confused about the page that I attached...

I don't understand part (ii)...

How can you compute X[T]X? So why is T(v_1)=v_2 and T(v_2)=av_1 + bv_2?

Thanks in advance...
 

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Hey Artusartos.

Are you just trying to find the linear transformation given those properties of how v1 and v2 maps to v1' and v2'?
 
chiro said:
Hey Artusartos.

Are you just trying to find the linear transformation given those properties of how v1 and v2 maps to v1' and v2'?


Hi,


I'm not trying to find anything. I was just trying to undestand the page that I attached (Part ii)...I don't understand why they wrote T(v_1) = v_2 and T(v_2) = av_1 + bv_2
 
I think (but am not certain) that this is just an example transformation.
 
chiro said:
I think (but am not certain) that this is just an example transformation.

Oh...so are they just making that up to give an example? I thought they were deriving those equations from somewhere, and that's why I was confused...
 
I'm pretty sure it is just an example.
 
chiro said:
I'm pretty sure it is just an example.

Ok thanks :)
 

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