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  3. 6 prove that pox1pixx1p2xxx2psxxx2x3 s a basis for p3 hint...

Question: 6 prove that pox1pixx1p2xxx2psxxx2x3 s a basis for p3 hint...

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6- Prove that (po(x)-1,pi(x)x-1,p2(x(x-)(x-2).ps(x)-(x(x2)(x3) s a basis for P3. Hint: You may use the following facts without proof: Fact 1: 1x is a basis for Ps,so dimPs 4. Fact 2: Let n 2 1 be an integer. A polynomial of degree n cannot be written as a linear combination of polynomials of degree at most n-1. Fact 3: Let v, Vp be a set of vectors in a vector space V. The set (v, Vp is linearly independent if and only if all the following conditions hold true: v2 is not a scalar multiple of v v3 is not a linear combination of vi and v2 v4 is not a linear combination of vi, v2, and v3 Vp is not a linear combination of vi,,vp Fact 4: Let V be a vector space of dimension n. Then any linearly independent set in V that has exactly n elements is a basis for V.

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