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a(x, y) represent the area of the parallelogram formed by the 2- mensional vectors X and y. Prove that if u and v are two 2-dimensional vectors and A is a 2 × 2 matrix, then a(Au, Av) = det(A)a(u, v).

a(x, y) represent the area of the parallelogram formed by the 2- mensional vectors X and y. Prove that if u and v are two 2-dimensional vectors and A is a 2 × 2 matrix, then a(Au, Av) = det(A)a(u, v).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let a(x, y) represent the area of the parallelogram formed by the 2-dimensional vectors x and y. Prove that if u and v are two 2-dimensional vectors and A is a 2 x 2 matrix, then a(Au, Av) = det(A)a(u, v).
Transcribed Image Text:1. Let a(x, y) represent the area of the parallelogram formed by the 2-dimensional vectors x and y. Prove that if u and v are two 2-dimensional vectors and A is a 2 x 2 matrix, then a(Au, Av) = det(A)a(u, v).
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