If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (2-1)³. (-3-t)², 1+18t-5t² +1³ Write the coordinate vector for the polynomial (2-t)³, denoted p₁. P₁ = FRIED
If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (2-1)³. (-3-t)², 1+18t-5t² +1³ Write the coordinate vector for the polynomial (2-t)³, denoted p₁. P₁ = FRIED
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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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 \((2-t)^3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f6f3ae-62d0-4ecf-a7d1-a70a7054db3c%2F8494336f-89d4-4ad8-b638-532f98b8d58c%2F28kfg7o_processed.jpeg&w=3840&q=75)
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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