Let u = (1, –3) and v = (2,5) in R². (a) Find (u, v) and ||v|| with respect to the standard inner product on R?. (b) Find (u, v) and ||v|| with respect to the inner product defined on R? by ((T1, 12), (Y1, Y2)) = x1Y1 – 201Y2 – 202Y1 + 5x2Y2. -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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for part a, please use the standard inner product, that is, the dot product on R^n

Let u =
(1, –3) and v =
(2,5) in R².
(a) Find (u, v) and ||v|| with respect to the standard inner product on R?.
(b) Find (u, v) and ||v|| with respect to the inner product defined on R? by
((T1, 12), (Y1, Y2)) = x1Y1 – 201Y2 – 202Y1 + 5x2Y2.
-
Transcribed Image Text:Let u = (1, –3) and v = (2,5) in R². (a) Find (u, v) and ||v|| with respect to the standard inner product on R?. (b) Find (u, v) and ||v|| with respect to the inner product defined on R? by ((T1, 12), (Y1, Y2)) = x1Y1 – 201Y2 – 202Y1 + 5x2Y2. -
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