(a) Let F:R n R n be an affine transformation. Let L 1 , L 2...

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(a) Let F:Rn → Rn be an affine transformation. Let L1, L⊂ Rbe 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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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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