Question: (a) Suppose A : R R is a (given) linear transformation. Prove that there exists a real number , depending only on A, such that

(a) Suppose A : R R is a (given) linear transformation. Prove that there exists a real number , depending only on A, such that A(x) = x for all x R. Is the number unique? (Justify your answer!) (b) Briefly explain (in words) what the assertion in part (a) is actually saying geometrically (i.e., as a shape)

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