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a) V = R", (x, y) = (Ax) · (Ay) where A e Mn,n is invertible.

a) V = R", (x, y) = (Ax) · (Ay) where A e Mn,n is invertible.

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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Are the following functions 〈·, ·〉 : V × V → R inner products?

a) V = R", (x, y) = (Ax) · (Ay) where A E Mn,n is invertible. b) Let T : P1 –→P1 defined by T(ax + b) = (4a – 26)x + b – 2a. V = P1, (p(x), q(x)) = Lo P(x)T(q(x))dæ Yes No
Transcribed Image Text:a) V = R", (x, y) = (Ax) · (Ay) where A E Mn,n is invertible. b) Let T : P1 –→P1 defined by T(ax + b) = (4a – 26)x + b – 2a. V = P1, (p(x), q(x)) = Lo P(x)T(q(x))dæ Yes No
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