The vectors listed in Eq. (10) are used in several of the exercise that follow. v 1 = 1 2 , v 2 = 2 3 , v 3 = 2 4 , v 4 = 1 1 , v 5 = 3 6 , u 0 = 1 0 0 , u 1 = 1 2 - 1 , u 2 = 2 1 - 3 , u 3 = - 1 4 3 , u 4 = 4 4 0 , u 5 = 1 1 0 In Exercises 1-14, use Eq.(6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector as a linear combination of the others. u 0 , u 1 , u 2 , u 4
The vectors listed in Eq. (10) are used in several of the exercise that follow. v 1 = 1 2 , v 2 = 2 3 , v 3 = 2 4 , v 4 = 1 1 , v 5 = 3 6 , u 0 = 1 0 0 , u 1 = 1 2 - 1 , u 2 = 2 1 - 3 , u 3 = - 1 4 3 , u 4 = 4 4 0 , u 5 = 1 1 0 In Exercises 1-14, use Eq.(6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector as a linear combination of the others. u 0 , u 1 , u 2 , u 4
Solution Summary: The author explains how to determine whether the given set of vectors leftmathbfu_0,
The vectors listed in Eq. (10) are used in several of the exercise that follow.
v
1
=
1
2
,
v
2
=
2
3
,
v
3
=
2
4
,
v
4
=
1
1
,
v
5
=
3
6
,
u
0
=
1
0
0
,
u
1
=
1
2
-
1
,
u
2
=
2
1
-
3
,
u
3
=
-
1
4
3
,
u
4
=
4
4
0
,
u
5
=
1
1
0
In Exercises 1-14, use Eq.(6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector as a linear combination of the others.
u
0
,
u
1
,
u
2
,
u
4
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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