1
f K V
Imf
= Imf
2
Kerf
= Kerf
2
V = Imf Kerf
A n
rank A + rank n(A I
n
)
f
R
3
ϕ(x, y, z) = (4x 2y + 2z, z,2x + 2 x + y + z)
f f
f

Preview text:

≥ 1 f K V Imf = Imf 2 Kerf = Kerf 2 V = Imf ⊕ Kerf A n rank A + rank (A − I ) ≥ n n f R3
ϕ(x, y, z) = (4x − 2y + 2z, 2x + 2z, −x + y + z) f f f