Orthonormal Sets in P 2 In Exercises 57-62, let p ( x ) = a 0 + a 1 x + a 2 x 2 and q ( x ) = b 0 + b 1 x + b 2 x 2 be vectors in P 2 with 〈 p , q 〉 = a 0 b 0 + a 1 b 1 + a 2 b 2 . Determine whether the polynomials form an orthonormal set, and if not, apply the Gram-Schmidt orthonormalization process to form an orthonormal set. { 1 + x 2 2 , − 1 + x + x 2 3 }
Orthonormal Sets in P 2 In Exercises 57-62, let p ( x ) = a 0 + a 1 x + a 2 x 2 and q ( x ) = b 0 + b 1 x + b 2 x 2 be vectors in P 2 with 〈 p , q 〉 = a 0 b 0 + a 1 b 1 + a 2 b 2 . Determine whether the polynomials form an orthonormal set, and if not, apply the Gram-Schmidt orthonormalization process to form an orthonormal set. { 1 + x 2 2 , − 1 + x + x 2 3 }
Solution Summary: The author explains that the polynomials form an orthonormal set, if not, then convert them.
Orthonormal Sets in
P
2
In Exercises 57-62, let
p
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
and
q
(
x
)
=
b
0
+
b
1
x
+
b
2
x
2
be vectors in
P
2
with
〈
p
,
q
〉
=
a
0
b
0
+
a
1
b
1
+
a
2
b
2
. Determine whether the polynomials form an orthonormal set, and if not, apply the Gram-Schmidt orthonormalization process to form an orthonormal set.
{
1
+
x
2
2
,
−
1
+
x
+
x
2
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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