Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let V be the set of all pairs (x, y) of real numbers together with the following
operations: (1, ₁) (x2, Y2) = (2x₁x2, Y₁ + 3y2) co (x, y) = (cx, 0).
1. Show that there exists an additive identity element, that is:
There exists (w, z) = V such that (x, y) & (w, z) = (x, y).
2. Explain why V nonetheless is not a vector space.
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Transcribed Image Text:Let V be the set of all pairs (x, y) of real numbers together with the following operations: (1, ₁) (x2, Y2) = (2x₁x2, Y₁ + 3y2) co (x, y) = (cx, 0). 1. Show that there exists an additive identity element, that is: There exists (w, z) = V such that (x, y) & (w, z) = (x, y). 2. Explain why V nonetheless is not a vector space.
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