Question

Consider the linearly independent set of vectors B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4, 1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4) in P4(R), does...

Consider the linearly independent set of vectors

B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4, 1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4)

in P4(R), does B form a basis for P4(R) and why?

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