PROBLEMS For Problems 1-14, determine the component vector of the given vector in the vector space V relative to the given ordered basis B . V = P 3 ( ℝ ) ; B = { x 3 + x 2 , x 3 − 1 , x 3 + 1 , x 3 + x } ; p ( x ) = 8 + x + 6 x 2 + 9 x 3 .
PROBLEMS For Problems 1-14, determine the component vector of the given vector in the vector space V relative to the given ordered basis B . V = P 3 ( ℝ ) ; B = { x 3 + x 2 , x 3 − 1 , x 3 + 1 , x 3 + x } ; p ( x ) = 8 + x + 6 x 2 + 9 x 3 .
Solution Summary: The author explains that the component vector is (6,-3,5,1).
For Problems 1-14, determine the component vector of the given vector in the vector space
V
relative to the given ordered basis
B
.
V
=
P
3
(
ℝ
)
;
B
=
{
x
3
+
x
2
,
x
3
−
1
,
x
3
+
1
,
x
3
+
x
}
;
p
(
x
)
=
8
+
x
+
6
x
2
+
9
x
3
.
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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