(a) Find a linear transformation T : R2 > R2 that reects a vector (say) across the yaxis. Give the matrix T(x) = Ax of this transformation, and...
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(a) Find a linear transformation T : R2 —> R2 that reflects a vector (say) across the y—axis. Give the matrix T(x) = Ax of this transformation, and draw the image of the unit square under this transformation. (b) Find a linear transformation 8 : R2 —> R2 that rotates a vector (xyy) counter— clockwise by 60°. Give the matrix S (x) = Bx of this transformation, and draw the image of the unit square under this transformation. (c) Find the matrix M representing the linear transformation that first rotates a vector as in (b), then reflects a vector as in (a), then rotates a vector by 60° clockwise. You may use your answers from (a) and (1)). Draw the image of the unit square under this transformation. ((1) Using the geometric descriptions of the transformations, without actually multi- plying them out, find the smallest positive integers In and k2 such that A'"1 = I and B"62 = 1. Using these, find the smallest positive integer k3 such that M *3 = I .

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Subject: Linear Algebra, Math
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