Given the d. space of polynomials of degree <3, (P3(R),+,-). To examine whether the vectors q₁=3x³-x²-1 and q2=x³+4x-1 belong to the d. subspace W=span{p₁,p2.p3}, where, p₁=2x³-x²+3x+2, p2=-x³+x²+x-3 and p3=x³+x²+9x-5. Then determine two bases of P3(R), one of which contains q₁ and the other 92. (Hint: use the coordinate vector of the vectors pi, ie {1,2,3} and qi, je {1,2} with respect to the normal basis of P3(R) and transfer the questions of the Exercise to the d. space (R4(R),+,.).

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