Question: (a) Let F:R n R n be an affine transformation. Let L 1 , L 2 R n be two parallel lines. Prove

(a) Let F:Rn → Rn be an affine transformation. Let L1, L2 ⊂ Rn be two parallel lines. Prove that F[L1] and F[L2] are also parallel lines.

(b) Is the converse valid: if F: Rn → Rn maps parallel lines to parallel lines, then F is necessarily an affine transformation?

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