Let L : V → W be a linear transformation, and let T be a subspace of W . The inverse image of T , denoted L − 1 ( T ) , is defined by L − 1 ( T ) = { v ∈ V | L ( v ) ∈ T } Show that L − 1 ( T ) is a subspace of V .
Let L : V → W be a linear transformation, and let T be a subspace of W . The inverse image of T , denoted L − 1 ( T ) , is defined by L − 1 ( T ) = { v ∈ V | L ( v ) ∈ T } Show that L − 1 ( T ) is a subspace of V .
Let
L
:
V
→
W
be a linear transformation, and let T be a subspace of W. The inverse image of T, denoted
L
−
1
(
T
)
, is defined by
L
−
1
(
T
)
=
{
v
∈
V
|
L
(
v
)
∈
T
}
Show that
L
−
1
(
T
)
is a subspace of V.
Differential Equations and Linear Algebra (4th Edition)
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