With respect to the basis B = { 1 , x , x 2 } for P 2 , find the coordinate vector for each of the following. a) p ( x ) = x 2 − x + 1 b) p ( x ) = x 2 + 4 x − 1 c) p ( x ) = 2 x + 5
With respect to the basis B = { 1 , x , x 2 } for P 2 , find the coordinate vector for each of the following. a) p ( x ) = x 2 − x + 1 b) p ( x ) = x 2 + 4 x − 1 c) p ( x ) = 2 x + 5
Solution Summary: The author explains that the coordinate vector for the second order polynomial is p(x) = 2-x+1 with respect to the basis of the vector space V of dimension
With respect to the basis
B
=
{
1
,
x
,
x
2
}
for
P
2
, find the coordinate vector for each of the following.
a)
p
(
x
)
=
x
2
−
x
+
1
b)
p
(
x
)
=
x
2
+
4
x
−
1
c)
p
(
x
)
=
2
x
+
5
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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