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Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. P, (t) = 2 + 7t, p2(t) = 6 + 2t – 2t°, p3 (t) = 2t – 21, p4(t) = - 12+ 23t – 812 + 6t° 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 which is row equivalent to I, and therefore does form a basis for R*. O B. The set of polynomials P, is isomorphic to R°, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. O C. The set of polynomials P, is isomorphic to R, which always has three vectors as a basis, so four polynomials cannot possibly be a basis. O D. The matrix represented by the coordinate vectors is which is not row equivalent to I, and therefore does not form a basis for R4. Therefore, the polynomials V form a basis for P, due to the isomorphism between Pa and R*. а) do b) do not exceeding the appropriate number of vectors. the isomorphism between P3 and R°.

Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. P, (t) = 2 + 7t, p2(t) = 6 + 2t – 2t°, p3 (t) = 2t – 21, p4(t) = - 12+ 23t – 812 + 6t° 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 which is row equivalent to I, and therefore does form a basis for R*. O B. The set of polynomials P, is isomorphic to R°, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. O C. The set of polynomials P, is isomorphic to R, which always has three vectors as a basis, so four polynomials cannot possibly be a basis. O D. The matrix represented by the coordinate vectors is which is not row equivalent to I, and therefore does not form a basis for R4. Therefore, the polynomials V form a basis for P, due to the isomorphism between Pa and R*. а) do b) do not exceeding the appropriate number of vectors. the isomorphism between P3 and R°.

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. P1 (t) = 2 + 7t, p2(t) = 6 + 2t - 2t°, p3 (t) = 2t – 21, P4(t) = - 12 + 23t – 812 + 6t° 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 which is row equivalent to I, and therefore does form a basis for R*. O B. The set of polynomials P, is isomorphic to R°, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. O C. The set of polynomials P, is isomorphic to R, which always has three vectors as a basis, so four polynomials cannot possibly be a basis. O D. The matrix represented by the coordinate vectors is which is not row equivalent to I, and therefore does not form a basis for R*. Therefore, the polynomials V form a basis for P, due to the isomorphism between P3 and R*. а) do b) do not exceeding the appropriate number of vectors. the isomorphism between P3 and R°.
Transcribed Image Text:Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. P1 (t) = 2 + 7t, p2(t) = 6 + 2t - 2t°, p3 (t) = 2t – 21, P4(t) = - 12 + 23t – 812 + 6t° 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 which is row equivalent to I, and therefore does form a basis for R*. O B. The set of polynomials P, is isomorphic to R°, which has three vectors as a basis. A set of four polynomials is a basis once one of the polynomials is discarded. O C. The set of polynomials P, is isomorphic to R, which always has three vectors as a basis, so four polynomials cannot possibly be a basis. O D. The matrix represented by the coordinate vectors is which is not row equivalent to I, and therefore does not form a basis for R*. Therefore, the polynomials V form a basis for P, due to the isomorphism between P3 and R*. а) do b) do not exceeding the appropriate number of vectors. the isomorphism between P3 and R°.
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