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  3. (3) consider the linear map ? : r2 ? r2 which send

(3) Consider the linear map ? : R2 ? R2 which sends (1, 0) ?? (?3,...

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Advance Math

(3) Consider the linear map ? : R2 ? R2 which sends (1, 0) ??(?3, 5) and (0, 1) ?? (4, ?1).

(a) What is the matrix of the transformation? What is the changeof coordinates matrix? Do they agree? How come?

(b) Where does this transformation send the area between thevector (4, 2) and the x-axis? Explain algebraically and draw apicture.

(c) What is the image of the lower half plane under ?? Explainalgebraically and draw a picture.

(d) What is the pre-image of the upper half plane under ??Explain algebraically and draw a picture.

(e) What is the image of the unit circle under ?? Explainalgebraically and draw a picture.

(f) Deduce whether or not linear transformations preserveangles/areas/curves/shapes, etc.

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