Let V be an two dimensional subspace of R 4 spanned by ( 0 , 1 , 0 , 1 ) and ( 0 , 2 , 0 , 0 ) . Write the vector u = ( 1 , 1 , 1 , 1 ) in the form u = v + w , where v is in V and w is orthogonal to every vector in V .
Let V be an two dimensional subspace of R 4 spanned by ( 0 , 1 , 0 , 1 ) and ( 0 , 2 , 0 , 0 ) . Write the vector u = ( 1 , 1 , 1 , 1 ) in the form u = v + w , where v is in V and w is orthogonal to every vector in V .
Solution Summary: The author explains that the vector u in the form of = v+w is (0,1,1,1) and w = orthogonal to every vector in
Let
V
be an two dimensional subspace of
R
4
spanned by
(
0
,
1
,
0
,
1
)
and
(
0
,
2
,
0
,
0
)
. Write the vector
u
=
(
1
,
1
,
1
,
1
)
in the form
u
=
v
+
w
, where
v
is in
V
and
w
is orthogonal to every vector in
V
.
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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