For Problems 12 − 13 , use the inner product ( 5.1.13 ) in Problem 11 to determine 〈 A , B 〉 , | | A | | , and | | B | | . Also, determine the angle between the given matrices. A = [ 3 2 − 2 4 ] , B = [ 1 1 − 2 1 ] . 11. Referring to A and B in Problem 8 , show that the mapping 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22 ( 5 . 1 . 13 ) defines a valid inner product on M 2 ( ℝ ) . A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ]
For Problems 12 − 13 , use the inner product ( 5.1.13 ) in Problem 11 to determine 〈 A , B 〉 , | | A | | , and | | B | | . Also, determine the angle between the given matrices. A = [ 3 2 − 2 4 ] , B = [ 1 1 − 2 1 ] . 11. Referring to A and B in Problem 8 , show that the mapping 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22 ( 5 . 1 . 13 ) defines a valid inner product on M 2 ( ℝ ) . A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ]
Solution Summary: The author explains how to determine the value of langle A,Brangle and the angle between the matrix A and B.
For Problems
12
−
13
, use the inner product
(
5.1.13
)
in Problem
11
to determine
〈
A
,
B
〉
,
|
|
A
|
|
, and
|
|
B
|
|
. Also, determine the angle between the given matrices.
A
=
[
3
2
−
2
4
]
,
B
=
[
1
1
−
2
1
]
.
11. Referring to
A
and
B
in Problem
8
, show that the mapping
〈
A
,
B
〉
=
a
11
b
11
+
a
12
b
12
+
a
21
b
21
+
a
22
b
22
(
5
.
1
.
13
)
defines a valid inner product on
M
2
(
ℝ
)
.
A
=
[
a
11
a
12
a
21
a
22
]
and
B
=
[
b
11
b
12
b
21
b
22
]
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