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Let S = {2x + 1, x – 3}. Use the definition of span to show span(S) = P1. Use the process to generate formulas for c, and c2. Check your results by using those formulas to write i = 7x – 14 in terms of the vectors in S. Write out every step. Show all work.

Let S = {2x + 1, x – 3}. Use the definition of span to show span(S) = P1. Use the process to generate formulas for c, and c2. Check your results by using those formulas to write i = 7x – 14 in terms of the vectors in S. Write out every step. Show all work.

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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Let \( S = \{2x + 1, x - 3\} \). Use the definition of span to show \(\text{span}(S) = \mathbb{P}_1\). Use the process to generate formulas for \( c_1 \) and \( c_2 \). Check your results by using those formulas to write \( \vec{v} = 7x - 14 \) in terms of the vectors in \( S \). Write out every step. **Show all work.**
Transcribed Image Text:Let \( S = \{2x + 1, x - 3\} \). Use the definition of span to show \(\text{span}(S) = \mathbb{P}_1\). Use the process to generate formulas for \( c_1 \) and \( c_2 \). Check your results by using those formulas to write \( \vec{v} = 7x - 14 \) in terms of the vectors in \( S \). Write out every step. **Show all work.**
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