Determine whether the following are linear transformations from C [ 0 , 1 ] into ℝ 1 : (a) L ( f ) = f ( 0 ) (b) L ( f ) = | f ( 0 ) | (c) L ( f ) = [ f ( 0 ) + f ( 1 ) ] / 2 (d) L ( f ) = { f 0 1 [ f ( x ) ] 2 d x } 1 / 2
Determine whether the following are linear transformations from C [ 0 , 1 ] into ℝ 1 : (a) L ( f ) = f ( 0 ) (b) L ( f ) = | f ( 0 ) | (c) L ( f ) = [ f ( 0 ) + f ( 1 ) ] / 2 (d) L ( f ) = { f 0 1 [ f ( x ) ] 2 d x } 1 / 2
Solution Summary: The author analyzes the given linear translation from Cleft[0,1right] into R1.
Determine whether the following are linear transformations from
C
[
0
,
1
]
into
ℝ
1
: (a)
L
(
f
)
=
f
(
0
)
(b)
L
(
f
)
=
|
f
(
0
)
|
(c)
L
(
f
)
=
[
f
(
0
)
+
f
(
1
)
]
/
2
(d)
L
(
f
)
=
{
f
0
1
[
f
(
x
)
]
2
d
x
}
1
/
2
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