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 3 − 2 x 4 = 0 x 2 + 2 x 3 − 3 x 4 = 0
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 3 − 2 x 4 = 0 x 2 + 2 x 3 − 3 x 4 = 0
Solution Summary: The author calculates the value of mathrmdim(W) when the vector x satisfies a given condition.
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
3
−
2
x
4
=
0
x
2
+
2
x
3
−
3
x
4
=
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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