Let V and V' be vector spaces over a field F and let f: V→ V' be a linear map. Which of the following statemens are correct? 0 O O D f is bijective if ker f = 0. f is surjective if Imf = V'. ker f is a subspace of V. f is injective if ker f = 0.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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Let V and V' be vector spaces over a field F and let f: V → V' be a linear map. Which
of the following statemens are correct?
0
0
0
f is bijective if ker f = 0.
f is surjective if Imf = V'.
ker f is a subspace of V.
f is injective if ker f = 0.
Transcribed Image Text:Let V and V' be vector spaces over a field F and let f: V → V' be a linear map. Which of the following statemens are correct? 0 0 0 f is bijective if ker f = 0. f is surjective if Imf = V'. ker f is a subspace of V. f is injective if ker f = 0.
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