Prove that { 1 , x , x 2 , ...... x n } is a linearly independent set in P n by supposing that p ( x ) = θ ( x ) , where p ( x ) = a 0 + a 1 x + a 2 x 2 ...... + a n x n . Next, take successive derivatives as in Example 2 .
Prove that { 1 , x , x 2 , ...... x n } is a linearly independent set in P n by supposing that p ( x ) = θ ( x ) , where p ( x ) = a 0 + a 1 x + a 2 x 2 ...... + a n x n . Next, take successive derivatives as in Example 2 .
Solution Summary: The author explains that in the polynomial of n degree the set left1,x,x2,mathrm...nright is linearly independent.
Prove that
{
1
,
x
,
x
2
,
......
x
n
}
is a linearly independent set in
P
n
by supposing that
p
(
x
)
=
θ
(
x
)
, where
p
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
......
+
a
n
x
n
. Next, take successive derivatives as in Example
2
.
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