Page 289 - 35Linear Algebra
P. 289
16.2 Image 289
Figure 16.1: For the function f : S → T, S is the domain, T is the tar-
get/codomain, f(S) is the range and f −1 (U) is the pre-image of U ⊂ T.
Since
1 0 1 2a 1 0 1 2a
RREF 0 1 1 a = 0 1 1 a
0 1 1 a 0 0 0 0
we have
2 −1
1
M −1 U = a + b −1 a ∈ [0, 1], b ∈ R ,
0 1
3
a strip from a plane in R .
16.2.1 One-to-one and Onto
The function f is one-to-one (sometimes denoted 1:1) if different elements
in S always map to different elements in T. That is, f is one-to-one if for
any elements x 6= y ∈ S, we have that f(x) 6= f(y), as pictured below.
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