Question on Linear Transformations with Lines and finding Natural Matrices.

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SUMMARY

The discussion focuses on linear transformations T and S defined as T(x, y) = (5x + y, 2x + 2y) and S(x, y) = (3x + 2y, x). The user seeks assistance in finding the image of the line 2x + 3y = 5 under transformation T and determining the natural matrices for the composite transformation T ∘ S and the inverse transformation T^-1. The user expresses difficulty in visualizing the transformation of a line, although they eventually received help from a peer.

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  • Knowledge of how to find the image of a line under a transformation
  • Concept of inverse transformations and their computation
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Wesc
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Let T : R2 -> R2 and S : R2 -> R2 be linear transformations de fined by:
T(x; y) = (5x + y ; 2x + 2y) and S(x; y) = (3x + 2y ; x):

(i). Find the image of the line 2x + 3y = 5 under T.
(ii). Find the natural matrices of the linear transformations T o S
and T^-1

Sorry, I haven't done this topic in 3 months now, and this question came up and I'm really struggling to come up with a solution. I drew out a graph to try to visualise what the answer could be, but again nothing seemed to work out :/ I mean, I can generally do transformation of a point questions fine, but have never come across transforming a line, so any help would be much appreciated, thanks.
 
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Nevermind, I got a solution off a friend.
 

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