b11 and B = b12 a12 A = 121 b21 b22 a22 are arbitrary vectors in R2X2, then the mapping (A, B) = a1b11 + aj2 b12 + a21 b21 + a22 b22 defines an inner product in R2X2. Use this inner product to determine (A, B), || A||, || B|| for 1 A = -3 and B = (A, B) = || || = || B|| =
b11 and B = b12 a12 A = 121 b21 b22 a22 are arbitrary vectors in R2X2, then the mapping (A, B) = a1b11 + aj2 b12 + a21 b21 + a22 b22 defines an inner product in R2X2. Use this inner product to determine (A, B), || A||, || B|| for 1 A = -3 and B = (A, B) = || || = || B|| =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Question
Use this inner product to determine ⟨A,B⟩, ‖A‖, ‖B‖
![a11
A =
a12
b12
and B =
а22
[b21 b22
a21
2x2
are arbitrary vectors in RX2, then the mapping
(A, B) = a11b11 + aj2b12 + a21b21 + am b22
2x2
defines an inner product in R²
Use this inner product to determine (A, B), || A||, || B|| for
5
A =
and B =
-2
(А, В) %—
|| A|| =
|| B| :](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456fc56d-6522-4d21-af4e-8101a918b824%2F19a33722-00bf-4923-a4e9-1720439e2d08%2F71g3bph_processed.png&w=3840&q=75)
Transcribed Image Text:a11
A =
a12
b12
and B =
а22
[b21 b22
a21
2x2
are arbitrary vectors in RX2, then the mapping
(A, B) = a11b11 + aj2b12 + a21b21 + am b22
2x2
defines an inner product in R²
Use this inner product to determine (A, B), || A||, || B|| for
5
A =
and B =
-2
(А, В) %—
|| A|| =
|| B| :
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