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Determine whether or not the polynomial p = 7X³ +25X² + 38X-5 is in the span of the following three polynomials P1 = 3X³ + 10X² +7X P2 = X³ + 3X²-2X+1 P3 = X³ + 1 in P3(R). If so, write p as a linear combination of P1, P2 and P3. Justify your answer.

Determine whether or not the polynomial p = 7X³ +25X² + 38X-5 is in the span of the following three polynomials P1 = 3X³ + 10X² +7X P2 = X³ + 3X²-2X+1 P3 = X³ + 1 in P3(R). If so, write p as a linear combination of P1, P2 and P3. Justify your answer.

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 or not the polynomial p = 7X³ + 25X2 + 38X-5 is in the span of the following three polynomials P1 = 3X³ + 10X² + 7X P2 = X³ + 3X²2X + 1 P3 = X³ + 1 in P3 (R). If so, write p as a linear combination of P1, P2 and p3. Justify your answer.
Transcribed Image Text:Determine whether or not the polynomial p = 7X³ + 25X2 + 38X-5 is in the span of the following three polynomials P1 = 3X³ + 10X² + 7X P2 = X³ + 3X²2X + 1 P3 = X³ + 1 in P3 (R). If so, write p as a linear combination of P1, P2 and p3. Justify your answer.
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Step 1: To check.

In this question, we will check the given polynomial is in span of the polynomials p1 ,p2 and p3.

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