Let S = {1 – x, 2 – 2x} C F(R, R). Consider the following possible proof (blue text) that S is linearly dependent: Suppose that (*) a(1 — г) + b(2 — 2.г) — 0. Since a = -2 and h = 1 is a solution to...

Hi, I need help with this problem, please. Thank you!

Extracted text: Let S = {1 – x, 2 – 2x} C F(R, R). Consider the following possible proof (blue text) that S is linearly dependent: Suppose that (*) a(1 — г) + b(2 — 2.г) — 0. Since a = -2 and h = 1 is a solution to (*), it follows that S is linearly dependent. Choose the response that best describes the argument above. O S is linearly dependent, but the proof is incorrect because we can't simply assume that a(1 – x) + b(2 – 2x) this statement must be proven. 0: O This proof can't be correct because S is linearly independent. O This proof would have correctly shown that S is linearly independent if the writer had written "linearly independent" instead of "linearly dependent" at the end of the last sentence. S is linearly dependent, but the proof is incorrect because it only gives one specific example of a solution to (*) instead of giving a general solution. O This is a correct proof that S is linearly dependent.