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4. (5 marks) Let P3 be the vector space of all real polynomials of degree at most 3. Let S₁ = {p Є P3 : p(x) = ax³ + bx, a, b = R}, S₂ = {p Є P3 : p(x) = bx³ + bx²,6 € R} and S3 = {p = P3 : p(x) = ax² + b, a,b€ R,6 ≥ 0}. Determine whether S1, S2 or S3 are vector subspaces of P3, giving full reasons for your answers. For those who are vector subspaces determine their dimension.

4. (5 marks) Let P3 be the vector space of all real polynomials of degree at most 3. Let S₁ = {p Є P3 : p(x) = ax³ + bx, a, b = R}, S₂ = {p Є P3 : p(x) = bx³ + bx²,6 € R} and S3 = {p = P3 : p(x) = ax² + b, a,b€ R,6 ≥ 0}. Determine whether S1, S2 or S3 are vector subspaces of P3, giving full reasons for your answers. For those who are vector subspaces determine their dimension.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Give accurate response. I am mostly confused with S2 and S3. does S2 contain the zero vector?

4. (5 marks) Let P3 be the vector space of all real polynomials of degree at most 3. Let S₁ = {p Є P3 : p(x) = ax³ + bx, a, b = R}, S₂ = {p Є P3 : p(x) = bx³ + bx²,6 € R} and S3 = {p = P3 : p(x) = ax² + b, a,b€ R,6 ≥ 0}. Determine whether S1, S2 or S3 are vector subspaces of P3, giving full reasons for your answers. For those who are vector subspaces determine their dimension.
Transcribed Image Text:4. (5 marks) Let P3 be the vector space of all real polynomials of degree at most 3. Let S₁ = {p Є P3 : p(x) = ax³ + bx, a, b = R}, S₂ = {p Є P3 : p(x) = bx³ + bx²,6 € R} and S3 = {p = P3 : p(x) = ax² + b, a,b€ R,6 ≥ 0}. Determine whether S1, S2 or S3 are vector subspaces of P3, giving full reasons for your answers. For those who are vector subspaces determine their dimension.
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