Transcribed Image Text: Suppose you are given the set A= {u =(0,1,2),v=(-1,0,0)}

Transcribed Image Text: Suppose you are given the set A= {u =(0,1,2),v=(-1,0,0)}.
Describe how you would combine A with a suitable vector from the set
B = {z=(-5,2,4), w= (0, 2,2), s = (3,3,6)} to obtain a generating set for R’.
Your answer should contain the following (according to order):
• the proof that u and v are linearly independent
• the reason why A cannot generate R³ by itself
the proof that any vector (x, y,z) eR’ can be written as a linear combination of
AU{your chosen vector from B} (i.e. {u, v, z} or {u, v, w} or {u, v, s})
Hint: Use my instruction in question 3 as a guide.
• the argument of whether either one of the two remaining vectors of B that you did not
choose might work as well or might not work at all (i.e. give reasons for your claim)

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