Consider the subspace U of R₁[X] given by U = {a+bx+cX² +dX³ +eX4:a+2c= 0 and b-3c=0} Find a basis for U and determine dim(U). Make sure to prove that your proposed basis is indeed a basis for U.

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Q: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

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A: See solution below

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A: Please check step 2 for the solution.!

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A: The correct option is option (e) 1 + 2x²   The detailed solution is as follows below:

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