Hi, me with a very detailed, step-by-step approach to the solution to this problem. I will be glad if your steps are easy self-explanatory. you

Hi, me with a very detailed, step-by-step approach to the solution to this problem. I will be glad if your steps are easy self-explanatory. you very much. Transcribed Image Text: Let f V > W be a linear map of vector spaces over K. Prove the following (if a
statement is wrong, make a correct statement and prove it):
un V, if f(u),f(u2), . ,f(un)
independent
(a) For any U1, U2
linearly independent, then
are
un are
(b) For any ui, U2,. .. , Un E V, if u1, U2, –
linearly independent,
un are
then f(u), f(u2),… ,f(un)
independent
(c) Each vector v E K5 defines a linear functional v* : K5 >K by
are
5
v” ()
(v, )}
for x Ε Κ*.
V;Xi E K
Let W Row(A) and define
W
v
(K) : v” (u) = 0 for all u
W
Get a basis for W

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