Let A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ] be vectors in M 2 ( R ) . Show that the mapping 〈 A , B 〉 = a 11 b 11 does not define a valid inner product on M 2 ( R ) . Which of the four properties of an inner product, if any, do hold? Justify your answer.
Let A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ] be vectors in M 2 ( R ) . Show that the mapping 〈 A , B 〉 = a 11 b 11 does not define a valid inner product on M 2 ( R ) . Which of the four properties of an inner product, if any, do hold? Justify your answer.
Let
A
=
[
a
11
a
12
a
21
a
22
]
and
B
=
[
b
11
b
12
b
21
b
22
]
be vectors in
M
2
(
R
)
. Show that the mapping
〈
A
,
B
〉
=
a
11
b
11
does not define a valid inner product on
M
2
(
R
)
. Which of the four properties of an inner product, if any, do hold? Justify your answer.
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.
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