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4. In the vector space P3(R), let S = {p1(x), p2(x), p3(x)}, where P1 (x) = 63x° + 19x² – 37x – 41, P2(x) = –189x3 – 57x2 + 111x + 123, P3 (x) = 45x – 26x² – 55x + 92. (a) Determine whether S is linearly independent. (b) Determine whether (S) = P3(R). (c) Find the dimension of (S).

4. In the vector space P3(R), let S = {p1(x), p2(x), p3(x)}, where P1 (x) = 63x° + 19x² – 37x – 41, P2(x) = –189x3 – 57x2 + 111x + 123, P3 (x) = 45x – 26x² – 55x + 92. (a) Determine whether S is linearly independent. (b) Determine whether (S) = P3(R). (c) Find the dimension of (S).

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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In the vector space P3(R), let S = {p1(x), P2(x), P3(x)}, where p1 (x) = 63x° + 19x² – 37x – 41, P2(x) = –189x – 57x² + 111x + 123, P3 (x) = 45x – 26x? – 55x + 92. (a) Determine whether S is linearly independent. (b) Determine whether (S) = P3(R). (c) Find the dimension of (S). 4.
Transcribed Image Text:In the vector space P3(R), let S = {p1(x), P2(x), P3(x)}, where p1 (x) = 63x° + 19x² – 37x – 41, P2(x) = –189x – 57x² + 111x + 123, P3 (x) = 45x – 26x? – 55x + 92. (a) Determine whether S is linearly independent. (b) Determine whether (S) = P3(R). (c) Find the dimension of (S). 4.
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