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Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. +31³ P₁ (t)=2+6t, p t, p₂ (t) = 5 + 2t − 3t³, p3 (t) = 2t-2t², p₁(t) = 1 + 20t-10t²+: Which of the following is a true statement? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The matrix represented by the coordinate vectors is not form a basis for R4. O B. The matrix represented by the coordinate vectors is form a basis for Rª , which is not row equivalent to 14 and therefore does which is row equivalent to 14 and therefore does OC. The set of polynomials P3 is isomorphic to R³, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. OD. The set of polynomials P3 is isomorphic to R³, which always has three vectors as a basis, so four polynomials cannot possibly be a basis.

Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. +31³ P₁ (t)=2+6t, p t, p₂ (t) = 5 + 2t − 3t³, p3 (t) = 2t-2t², p₁(t) = 1 + 20t-10t²+: Which of the following is a true statement? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The matrix represented by the coordinate vectors is not form a basis for R4. O B. The matrix represented by the coordinate vectors is form a basis for Rª , which is not row equivalent to 14 and therefore does which is row equivalent to 14 and therefore does OC. The set of polynomials P3 is isomorphic to R³, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. OD. The set of polynomials P3 is isomorphic to R³, which always has three vectors as a basis, so four polynomials cannot possibly be a basis.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. +31³ P₁ (t)=2+6t, p t, p₂ (t) = 5 + 2t − 3t³, p3 (t) = 2t-2t², p₁(t) = 1 + 20t-10t²+: Which of the following is a true statement? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The matrix represented by the coordinate vectors is not form a basis for R4. O B. The matrix represented by the coordinate vectors is form a basis for Rª , which is not row equivalent to 14 and therefore does which is row equivalent to 14 and therefore does OC. The set of polynomials P3 is isomorphic to R³, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. OD. The set of polynomials P3 is isomorphic to R³, which always has three vectors as a basis, so four polynomials cannot possibly be a basis.
Transcribed Image Text:Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. +31³ P₁ (t)=2+6t, p t, p₂ (t) = 5 + 2t − 3t³, p3 (t) = 2t-2t², p₁(t) = 1 + 20t-10t²+: Which of the following is a true statement? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The matrix represented by the coordinate vectors is not form a basis for R4. O B. The matrix represented by the coordinate vectors is form a basis for Rª , which is not row equivalent to 14 and therefore does which is row equivalent to 14 and therefore does OC. The set of polynomials P3 is isomorphic to R³, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. OD. The set of polynomials P3 is isomorphic to R³, which always has three vectors as a basis, so four polynomials cannot possibly be a basis.
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