(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c). (e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y) below. = Ay where A is as (f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as below. 6 1 0 A = 16 0 0 08/3 For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
(d) sin(x) and cos²(x) in C([-T, π]) with the inner-product from (c). (e) (1,2,3) and (−1, 1, 1) in R³ with the inner-product (y) below. = Ay where A is as (f) (1,2,3) and (1, 1, −2) in R³ with the the inner-product (˜|y) = x³ Aỹ where A is as below. 6 1 0 A = 16 0 0 08/3 For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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