Question

If V is a vector space of polynomials of degree n with real numbers as coefficients,...

If V is a vector space of polynomials of degree n with real numbers as coefficients, over R, and W is generated by

the polynomials (x 3 + 2x 2 − 2x + 1, x3 + 3x 2 − x + 4, 2x 3 + x 2 − 7x − 7),

then is W a subspace of V , and if so, determine its basis.

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