Let f: RR. Prove that (a) f is linear f(ar+By) = af (a) +3f (y) for...

 

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Let f: R"R". Prove that (a) f is linear f(ar+By) = af (a) +3f (y) for all r, y = R" and all a, 3 € R. 4 marks (b) If f: R → Rm is linear, is f necessarily one-to-one? If so, prove this. If not, provide an example. 2 marks Let f: R"R". Prove that (a) f is linear f(ar+By) = af (a) +3f (y) for all r, y = R" and all a, 3 € R. 4 marks (b) If f: R → Rm is linear, is f necessarily one-to-one? If so, prove this. If not, provide an example. 2 marks