Give an alternate proof that { 1 , x , x 2 } is a linearly independent set in P 2 as follows: Let p ( x ) = a 0 + a 1 x + a 2 x 2 , and suppose that p ( x ) = θ ( x ) . Then p ( − 1 ) = 0 , p ( 0 ) = 0 , and p ( 1 ) = 0 . These three equations can be used to show that a 0 = a 1 = a 2 = 0 .
Give an alternate proof that { 1 , x , x 2 } is a linearly independent set in P 2 as follows: Let p ( x ) = a 0 + a 1 x + a 2 x 2 , and suppose that p ( x ) = θ ( x ) . Then p ( − 1 ) = 0 , p ( 0 ) = 0 , and p ( 1 ) = 0 . These three equations can be used to show that a 0 = a 1 = a 2 = 0 .
Solution Summary: The author explains how the set left1,x,x2right is a linearly independent set.
Give an alternate proof that
{
1
,
x
,
x
2
}
is a linearly independent set in
P
2
as follows: Let
p
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
, and suppose that
p
(
x
)
=
θ
(
x
)
. Then
p
(
−
1
)
=
0
,
p
(
0
)
=
0
, and
p
(
1
)
=
0
. These three equations can be used to show that
a
0
=
a
1
=
a
2
=
0
.
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