An inner product and an associated norm are defined on R² by the weighted scalar product where u = (2) and v = (u, v) 2u1v1 + 3u₂ v₂ = Let a = (²) and b = (a) Calculate (a, b), (a, a) and ||a|| (aa) b (b) Calculate the vector ca- (a,b) (c) Verify that, with respect to this inner product, the vector c is orthogonal to the vector a, but c is not orthogonal to the vector b
An inner product and an associated norm are defined on R² by the weighted scalar product where u = (2) and v = (u, v) 2u1v1 + 3u₂ v₂ = Let a = (²) and b = (a) Calculate (a, b), (a, a) and ||a|| (aa) b (b) Calculate the vector ca- (a,b) (c) Verify that, with respect to this inner product, the vector c is orthogonal to the vector a, but c is not orthogonal to the vector b
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
Question
100%
![An inner product and an associated norm are defined on R² by the weighted scalar
product
where u = (2) and v =
(u, v) 2u1v1 + 3u₂ v₂
=
Let a =
(²)
and b =
(a) Calculate (a, b), (a, a) and ||a||
(aa) b
(b) Calculate the vector ca-
(a,b)
(c) Verify that, with respect to this inner product, the vector c is orthogonal to the
vector a, but c is not orthogonal to the vector b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf33b320-4f7b-4a3b-8829-c5f41cb7c71a%2F01df57cd-572b-4a35-a547-335349d5885c%2Fqcor2z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An inner product and an associated norm are defined on R² by the weighted scalar
product
where u = (2) and v =
(u, v) 2u1v1 + 3u₂ v₂
=
Let a =
(²)
and b =
(a) Calculate (a, b), (a, a) and ||a||
(aa) b
(b) Calculate the vector ca-
(a,b)
(c) Verify that, with respect to this inner product, the vector c is orthogonal to the
vector a, but c is not orthogonal to the vector b
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