Math 2331
Linear Algebra
Section 7.1
Linear Transformations Part 1
Let V and W be vector spaces. A function
:
f
V
W
→
is called a linear transformation if
the following conditions hold
1. For all x and y in V,
f(x+y) = f(x) + f(y)
2. For all x in V and all scalars k,
f(kx) = k f(x)
These conditions are called "preserving the operations" because
Decide whether the following maps are linear transformations -
Example 1: Let
be defined by
:
f
→
\
\
( )
3
f
x
x
=
.
Example 2: Let
be defined by
:
f
→
\
\
( )
1
f
x
x
=
+

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