Let P3 be the vector space of polynomials of degree at most 3, and let S = {p1(x), p2(x), p3(x), p be a subset of P3 given by P1 (x) =4 – x + x³, P2(x) =1 + 2x – 3x2, - P3(x) =3 – 3x+ 3x? + x³, P4(x) =x – x³. (a) Determine whether the set S' spans P3. (b) Determine whether the set S is linearly independent. (c) Find a subset of S that is a basis for the vector space W = span (S). (d) Find the dimension of W.

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A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplicatior…

A: ANSWER :

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Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplication…

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Q: (b) Define subset W in R³ as W = {[x1,x2, x3]|4x1 – x2 + 5x3 = 0}. W is a subspace of R3 -

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Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplication…

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Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplication…

A: The answer is given below

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A: To find whether the polynomials are independent

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A: Let's find.

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A: 3. False  Because null polynomial is not a polynomial of degree exactly 3.

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A: The detailed solution of the problem is given in the next steps.

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A: it is not closed under addition.

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