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 = { 1 , 1 + x , 1 + x + x 2 , 1 + x + x 2 + x 3 } ; p ( x ) = 4 − x + x 2 − 2 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 = { 1 , 1 + x , 1 + x + x 2 , 1 + x + x 2 + x 3 } ; p ( x ) = 4 − x + x 2 − 2 x 3 .
Solution Summary: The author explains the component vector of v relative to the ordered basis B.
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
=
{
1
,
1
+
x
,
1
+
x
+
x
2
,
1
+
x
+
x
2
+
x
3
}
;
p
(
x
)
=
4
−
x
+
x
2
−
2
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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