Let Q be the basis for P 2 given in Exercise 26 . Find [ p ( x ) ] Q for p ( x ) = a 0 + a 1 x + a 2 x 2 . In P 2 , let Q = { p 1 ( x ) , p 2 ( x ) , p 3 ( x ) } , where p 1 ( x ) = β 1 + x + 2 x 2 , p 2 ( x ) = x + 3 x 2 , and p 3 ( x ) = 1 + 2 x + 8 x 2 . Use the basis B = { 1 , x , x 2 } to show that Q is a basis for P 2 .
Let Q be the basis for P 2 given in Exercise 26 . Find [ p ( x ) ] Q for p ( x ) = a 0 + a 1 x + a 2 x 2 . In P 2 , let Q = { p 1 ( x ) , p 2 ( x ) , p 3 ( x ) } , where p 1 ( x ) = β 1 + x + 2 x 2 , p 2 ( x ) = x + 3 x 2 , and p 3 ( x ) = 1 + 2 x + 8 x 2 . Use the basis B = { 1 , x , x 2 } to show that Q is a basis for P 2 .
Solution Summary: The author explains how to find the coordinate vector (x)_Q.
Let
Q
be the basis for
P
2
given in Exercise
26
. Find
[
p
(
x
)
]
Q
for
p
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
.
In
P
2
, let
Q
=
{
p
1
(
x
)
,
p
2
(
x
)
,
p
3
(
x
)
}
,
where
p
1
(
x
)
=
−
1
+
x
+
2
x
2
,
p
2
(
x
)
=
x
+
3
x
2
, and
p
3
(
x
)
=
1
+
2
x
+
8
x
2
. Use the basis
B
=
{
1
,
x
,
x
2
}
to show that
Q
is a basis for
P
2
.
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