In Exercises 1 − 8 , let W be the subspace of R 4 consisting of vectors of the form x = [ x 1 x 2 x 3 x 4 ] Find a basis for W when the components of x satisfy the given conditions. x 1 + x 2 − x 3 = 0 x 2 − x 4 = 0
In Exercises 1 − 8 , let W be the subspace of R 4 consisting of vectors of the form x = [ x 1 x 2 x 3 x 4 ] Find a basis for W when the components of x satisfy the given conditions. x 1 + x 2 − x 3 = 0 x 2 − x 4 = 0
In Exercises
1
−
8
, let
W
be the subspace of
R
4
consisting of vectors of the form
x
=
[
x
1
x
2
x
3
x
4
]
Find a basis for
W
when the components of
x
satisfy the given conditions.
x
1
+
x
2
−
x
3
=
0
x
2
−
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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