Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the second line have a one-to-one correspondence with points on first line

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.3: Properties Of Determinants
Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
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Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the second line have a one-to-one correspondence with points on first line

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