With respect to the basis B = { E 11 , E 12 , E 21 , E 22 } for the vector space V of all ( 2 × 2 ) matrices, find the coordinate vector for each of the following. a) A 1 = [ 2 − 1 3 2 ] b) A 2 = [ 1 0 − 1 1 ] c) A 3 = [ 2 3 0 0 ]
With respect to the basis B = { E 11 , E 12 , E 21 , E 22 } for the vector space V of all ( 2 × 2 ) matrices, find the coordinate vector for each of the following. a) A 1 = [ 2 − 1 3 2 ] b) A 2 = [ 1 0 − 1 1 ] c) A 3 = [ 2 3 0 0 ]
Solution Summary: The author explains how to find the coordinate vector for the matrix A_1=left[cc2& -1 3& 2
With respect to the basis
B
=
{
E
11
,
E
12
,
E
21
,
E
22
}
for the vector space
V
of all
(
2
×
2
)
matrices, find the coordinate vector for each of the following.
a)
A
1
=
[
2
−
1
3
2
]
b)
A
2
=
[
1
0
−
1
1
]
c)
A
3
=
[
2
3
0
0
]
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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