Consider the linear application f: R → R? such that (1,0,0)" E ker(f), f(0,1,0)T = (1, 2) %3D Select one or more: a.f is injective ; b. The image has dimension 21 c. The image of f does not contain 0 d. f(1,0,0)T = (1, 4) e. The kernel of f has dimension 2 f.f(1, 1, 1)T = (3, 3)": g. The kernel of f has dimension h. fjs surjective

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is the complete question plz have a look it has not any more Condtion. And choose 4 answers because 4 options are correct and provide complete soloutions
Consider the linear application
f: R3
(1,0,0)T E ker(f), f(0, 1,0)" = (1, 2)
R? such that
%3D
Select one or more:
a. f is injective,
b. The image has dimension 21
c. The image of f does not contain 0
d. f(1,0,0)" = (1,4)
e. The kernel of f has dimension 2
f. f(1, 1, 1)" = (3, 3)":
g. The kernel of f has dimension
1.
h. fjs surjective
16
Transcribed Image Text:Consider the linear application f: R3 (1,0,0)T E ker(f), f(0, 1,0)" = (1, 2) R? such that %3D Select one or more: a. f is injective, b. The image has dimension 21 c. The image of f does not contain 0 d. f(1,0,0)" = (1,4) e. The kernel of f has dimension 2 f. f(1, 1, 1)" = (3, 3)": g. The kernel of f has dimension 1. h. fjs surjective 16
Consider the linear application
f : R³ → R? such that
(1,0, 0)" E ker(f), f(0, 1, 0)" = (1, 2)
Select one or more:
a. f is injective
b. The image has dimension 2
O c. The image of f does not contain 0
O d. f(1,0,0)" = (1,4)T
%3D
e. The kernel of f has dimension 2
O f. f(1, 1, 1)" = (3, 3)T
%3D
g. The kernel of f has dimension 1 v
h. f is surjective
Transcribed Image Text:Consider the linear application f : R³ → R? such that (1,0, 0)" E ker(f), f(0, 1, 0)" = (1, 2) Select one or more: a. f is injective b. The image has dimension 2 O c. The image of f does not contain 0 O d. f(1,0,0)" = (1,4)T %3D e. The kernel of f has dimension 2 O f. f(1, 1, 1)" = (3, 3)T %3D g. The kernel of f has dimension 1 v h. f is surjective
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