Question: (a) Let m N be such that m 2. Suppose A : R R m is a (vector-valued) linear transformation. Prove that there exists an

(a) Let m N be such that m 2. Suppose A : R R m is a (vector-valued) linear transformation. Prove that there exists an vector v R m, depending only on A, such that A(c) = cv for all c R. Is the vector v unique? (Justify your answer!) (b) Briefly explain (in words) what the geometric representation of (the graph of) the transformation A is in the space R m.

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