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## Main Question or Discussion Point

I can't solve a problem about subspaces. Help would be great!

U and V are subspaces in the vector space R^4[x] given with:

U={p(x)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4; a1+a2+a3+a4=0, a1+a2+2a3+2a4=0, a0+a1=a3+a4}

V=L{x^3-x^2+x, x^4+1}

Find the dimensions and basis for U, U+V and U?V. Is the expresion 1-x+x^2-x^3+x^4 an element of U+V or U?V?

Thanks for your answers.

U and V are subspaces in the vector space R^4[x] given with:

U={p(x)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4; a1+a2+a3+a4=0, a1+a2+2a3+2a4=0, a0+a1=a3+a4}

V=L{x^3-x^2+x, x^4+1}

Find the dimensions and basis for U, U+V and U?V. Is the expresion 1-x+x^2-x^3+x^4 an element of U+V or U?V?

Thanks for your answers.