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7. Find a basis (po(x),..., Pn(x)) for the vector space Pn(F) such that each p; (x) is a polynomial of degree n. Justify your answer.

7. Find a basis (po(x),..., Pn(x)) for the vector space Pn(F) such that each p; (x) is a polynomial of degree n. 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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Can you answer #7.
**7.** Find a basis \((p_0(x), \ldots, p_n(x))\) for the vector space \(P_n(F)\) such that each \(p_i(x)\) is a polynomial of degree \(n\). Justify your answer. **8.** Prove that a vector space \(V\) is infinite-dimensional if and only if \(V\) contains an infinite linearly dependent subset.
Transcribed Image Text:**7.** Find a basis \((p_0(x), \ldots, p_n(x))\) for the vector space \(P_n(F)\) such that each \(p_i(x)\) is a polynomial of degree \(n\). Justify your answer. **8.** Prove that a vector space \(V\) is infinite-dimensional if and only if \(V\) contains an infinite linearly dependent subset.
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