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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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| :
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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