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Consider the following linear transformations of the plane:
T1 = “vertical shear with factor 1”
T2 = “90 degree anti-clockwise rotation ”
T3 = “reflection across the y-axis”
(a) Write down the matrices A1, A2, A3 that correspond to the respective transformations.
(b) Use matrix multiplication to determine the combined geometric effect of T1
followed by T2 followed by T3. Sketch the image of the unit square in the first
quadrant under this combined transformation.
(c) Use matrix multiplication to determine the combined geometric effect of T3
followed by T2 followed by T1, and compare it with the result from (b).

Sagot :

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