Showing That a Function Is an Inner Product In Exercises 27 and 28, let A = [ a 1 1 a 1 2 a 2 1 a 2 2 ] and B = [ b 1 1 b 1 2 b 2 1 b 2 2 ] be matrices in the vector space M 2 , 2 . Show that the function defines an inner product on M 2 , 2 . 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22
Showing That a Function Is an Inner Product In Exercises 27 and 28, let A = [ a 1 1 a 1 2 a 2 1 a 2 2 ] and B = [ b 1 1 b 1 2 b 2 1 b 2 2 ] be matrices in the vector space M 2 , 2 . Show that the function defines an inner product on M 2 , 2 . 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22
Solution Summary: The author explains that the given function defines an inner product on the vector space M_2,2.
Showing That a Function Is an Inner Product In Exercises 27 and 28, let
A
=
[
a
1
1
a
1
2
a
2
1
a
2
2
]
and
B
=
[
b
1
1
b
1
2
b
2
1
b
2
2
]
be matrices in the vector space
M
2
,
2
. Show that the function defines an inner product on
M
2
,
2
.
〈
A
,
B
〉
=
a
11
b
11
+
a
12
b
12
+
a
21
b
21
+
a
22
b
22
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
DISCRETE MATH: PLEASE PROVIDE ANSWER AND EXPLAIN.
Let A={1,2,3,4} and B={a,b,c,d}
(a) Construct an example of a function f:A→B that is a bijection.
(b) Is it true that every function g:A→B is a bijection? Briefly explain.
Abstract Algebra I
Let A = {1, 2, 3, 4} and let f:A ->A be defined as {(1, 3), (2, 4), (3, 1), (4, 3)}.
Is f injective? Explain. Is f surjective? Explain.
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