(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, L₂⊂ Rⁿbe 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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Question Posted: Apr 30, 2023 02:56 AM

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

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a An affine transformation F Rn Rn is defined as Fx Ax b where A is an n x n matrix and b is a vecto...View the full answer

Applied Linear Algebra

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