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# Invariant Lines and Line of Invaraint Points (FP4) watch

1. The transformation S is a shear with Matrix M =
( -1 2 )
( -2 3 )

Points (x, y) are mapped under S to image (x', y') such that

(x', y') = M(x, y)

Show that all the lines of the form y = x + c, where c is a constant, are invariant lines of S.
Probably easy question but I don't know how to find invariant lines Could somebody help?
Cheers.
2. You know that M(x,y) = (x',y'), and are asked to show that the line y = x + c is invariant, i.e. that if y = x + c, then y' = x' + c. In practice, y = x + c means that we are working with the vector (x, x+c). Find the image of this under M, and it'll hopefully be of the form (x', x'+c).

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