In Exercises 15-20, W is a subspace of R 4 consisting of vectors of the form x = [ x 1 x 2 x 3 x 4 ] Determine dim ( W ) when the components of x satisfy the given conditions. x 1 = β x 4 x 2 = 3 x 4 x 3 = 2 x 4
In Exercises 15-20, W is a subspace of R 4 consisting of vectors of the form x = [ x 1 x 2 x 3 x 4 ] Determine dim ( W ) when the components of x satisfy the given conditions. x 1 = β x 4 x 2 = 3 x 4 x 3 = 2 x 4
Solution Summary: The author explains that mathrmdim(W) is a subset of
In Exercises 15-20,
W
is a subspace of
R
4
consisting of vectors of the form
x
=
[
x
1
x
2
x
3
x
4
]
Determine
dim
(
W
)
when the components of
x
satisfy the given conditions.
x
1
=
−
x
4
x
2
=
3
x
4
x
3
=
2
x
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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