Let S = {1, x, x²} C F(R, R). Consider the following possible proof (blue text) that S is linearly independent: Suppose that (*) a + bx + cx² 0. Since a = 6 = c = 0 is a solution to (*), it follows...

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Extracted text: Let S = {1, x, x²} C F(R, R). Consider the following possible proof (blue text) that S is linearly independent: Suppose that (*) a + bx + cx² 0. Since a = 6 = c = 0 is a solution to (*), it follows that S is linearly independent. Choose the response that best describes the argument above. O This is a correct proof that S is linearly independent. S is linearly independent, but the proof is incorrect because we can't just assume that a + br + cr? 0; this statement must be proven. O This argument would have correctly shown that S is linearly dependent if the writer had written "linearly dependent" instead of "linearly independent" at the end of the last sentence. O This proof can't be correct because S is linearly dependent. O S is linearly independent, but the proof is incorrect because the argument doesn't show that a = b = c= 0 is the only solution to (*).