3. Let be a real number and let sin(6 x1 = sin( x2 = cos(0) (a) Show that B = (1, 2) is an orthonormal basis of R². (b) Given a vector y = Y2 ER², write it as a linear combination c₁₁ + €22. (Hint: find the transition matrix [Id].) (c) Verify Parseval's identity in this case: c² + c² = ||y||² = y² + y².
3. Let be a real number and let sin(6 x1 = sin( x2 = cos(0) (a) Show that B = (1, 2) is an orthonormal basis of R². (b) Given a vector y = Y2 ER², write it as a linear combination c₁₁ + €22. (Hint: find the transition matrix [Id].) (c) Verify Parseval's identity in this case: c² + c² = ||y||² = y² + y².
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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![3. Let be a real number and let
sin(6
x1 =
sin(
x2 =
cos(0)
(a) Show that B = (1, 2) is an orthonormal basis of R².
(b) Given a vector y =
Y2
ER², write it as a linear combination c₁₁ + €22.
(Hint: find the transition matrix [Id].)
(c) Verify Parseval's identity in this case:
c² + c² = ||y||² = y² + y².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09e653ae-bec3-48d5-82fe-0f606eb24e14%2F3c21679a-d54b-47a5-9c2c-35b80838a107%2Fjlhdgrb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let be a real number and let
sin(6
x1 =
sin(
x2 =
cos(0)
(a) Show that B = (1, 2) is an orthonormal basis of R².
(b) Given a vector y =
Y2
ER², write it as a linear combination c₁₁ + €22.
(Hint: find the transition matrix [Id].)
(c) Verify Parseval's identity in this case:
c² + c² = ||y||² = y² + y².
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