If are arbitrary vectors in R2x2, then the mapping A = (A, B) || A|| = ||B| = [a11 a12] a21 a22 A = and B = (A, B) = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in R2x2. Use this inner product to determine (A, B), || A||, || B||, and the angle A,B between A and B for [b11 b12] b21 b22 and B = -4 1 1 -5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If
are arbitrary vectors in R2x2, then the mapping
(A, B)
||A|| =
|| B||
A,B
A =
(radians).
[a11 a12]
a21 a22
(A, B) = a11b11 + a12b12 + a21b21 + a22b22
defines an inner product in R2X2. Use this inner product to determine (A, B), ||A||, ||B||, and the angle A,B between A and B for
13
A =
and B =
[b11 b12]
[b21 b22
and B =
-4 1
1 -5
Transcribed Image Text:If are arbitrary vectors in R2x2, then the mapping (A, B) ||A|| = || B|| A,B A = (radians). [a11 a12] a21 a22 (A, B) = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in R2X2. Use this inner product to determine (A, B), ||A||, ||B||, and the angle A,B between A and B for 13 A = and B = [b11 b12] [b21 b22 and B = -4 1 1 -5
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