Find the kernel and range of each of the following linear operators on P 3 : (a) L ( p ( x ) ) = x p ' ( x ) (b) L ( p ( x ) ) = p ( x ) − p ' ( x ) (c) L ( p ( x ) ) = p ( 0 ) x + p ( 1 )
Find the kernel and range of each of the following linear operators on P 3 : (a) L ( p ( x ) ) = x p ' ( x ) (b) L ( p ( x ) ) = p ( x ) − p ' ( x ) (c) L ( p ( x ) ) = p ( 0 ) x + p ( 1 )
Find the kernel and range of each of the following linear operators on
P
3
: (a)
L
(
p
(
x
)
)
=
x
p
'
(
x
)
(b)
L
(
p
(
x
)
)
=
p
(
x
)
−
p
'
(
x
)
(c)
L
(
p
(
x
)
)
=
p
(
0
)
x
+
p
(
1
)
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