Let V be the vector space of all ( 2 × 2 ) matrices and let S = { A 1 , A 2 , A 3 , A 4 } where, A 1 = [ 1 2 − 1 3 ] A 2 = [ − 2 1 2 − 1 ] A 3 = [ − 1 − 1 1 − 3 ] , and A 4 = [ − 2 2 2 0 ] As, in Example 8 , find a basis for S p ( S ) .
Let V be the vector space of all ( 2 × 2 ) matrices and let S = { A 1 , A 2 , A 3 , A 4 } where, A 1 = [ 1 2 − 1 3 ] A 2 = [ − 2 1 2 − 1 ] A 3 = [ − 1 − 1 1 − 3 ] , and A 4 = [ − 2 2 2 0 ] As, in Example 8 , find a basis for S p ( S ) .
Solution Summary: The author explains the basis for Sp(S).
Let
V
be the vector space of all
(
2
×
2
)
matrices and let
S
=
{
A
1
,
A
2
,
A
3
,
A
4
}
where,
A
1
=
[
1
2
−
1
3
]
A
2
=
[
−
2
1
2
−
1
]
A
3
=
[
−
1
−
1
1
−
3
]
, and
A
4
=
[
−
2
2
2
0
]
As, in Example
8
, find a basis for
S
p
(
S
)
.
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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