In Exercise 9-17, W is a subset of R 3 consisting of vectors of the form x = [ x 1 x 2 x 3 ] In each case, determine whether W is a subspace of R 2 . If W is a subspace, then give a geometric description of W . W = { x : x 2 = x 3 + x 1 }
In Exercise 9-17, W is a subset of R 3 consisting of vectors of the form x = [ x 1 x 2 x 3 ] In each case, determine whether W is a subspace of R 2 . If W is a subspace, then give a geometric description of W . W = { x : x 2 = x 3 + x 1 }
Solution Summary: The author explains that W is a subspace of R3, and the geometric description is shown in figure.
In Exercise 9-17,
W
is a subset of
R
3
consisting of vectors of the form
x
=
[
x
1
x
2
x
3
]
In each case, determine whether
W
is a subspace of
R
2
. If
W
is a subspace, then give a geometric description of
W
.
W
=
{
x
:
x
2
=
x
3
+
x
1
}
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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