3. [6 points] Consider the vector space V = P, over the field of real numbers F = R. Is the vector 4 – x – x² in the span of the vectors %3D 1+ 2x, x – x², -1+x+x² Explain why or why not. Show your calculations.

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3. [6 points] Consider the vector space V = P2 over the field of real numbers F = R.
Is the vector 4 – x – x² in the span of the vectors
1+ 2x, x – x², -1+x+x²
Explain why or why not. Show your calculations.
Transcribed Image Text:3. [6 points] Consider the vector space V = P2 over the field of real numbers F = R. Is the vector 4 – x – x² in the span of the vectors 1+ 2x, x – x², -1+x+x² Explain why or why not. Show your calculations.
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