Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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6) please help with p1, p2, p3, and if they are independent or dependent.
![If \( B \) is the standard basis of the space \( \mathbb{P}_3 \) of polynomials, then let \( B = \{1, t, t^2, t^3\} \). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work.
\[
(2-t)^3, \, (-3-t)^2, \, 1 + 18t - 5t^2 + t^3
\]
---
Write the coordinate vector for the polynomial \((2-t)^3\), denoted \( \mathbf{p}_1 \).
\[
\mathbf{p}_1 =
\]
Note: The blank space next to \(\mathbf{p}_1\) is intended for writing the coordinate vector corresponding to the polynomial \((2-t)^3\).](https://content.bartleby.com/qna-images/question/08f6f3ae-62d0-4ecf-a7d1-a70a7054db3c/8494336f-89d4-4ad8-b638-532f98b8d58c/28kfg7o_processed.jpeg)
Transcribed Image Text:If \( B \) is the standard basis of the space \( \mathbb{P}_3 \) of polynomials, then let \( B = \{1, t, t^2, t^3\} \). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work.
\[
(2-t)^3, \, (-3-t)^2, \, 1 + 18t - 5t^2 + t^3
\]
---
Write the coordinate vector for the polynomial \((2-t)^3\), denoted \( \mathbf{p}_1 \).
\[
\mathbf{p}_1 =
\]
Note: The blank space next to \(\mathbf{p}_1\) is intended for writing the coordinate vector corresponding to the polynomial \((2-t)^3\).
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