4. Determine whether or not the following functions are linearly independent in the vector space P4. {p:(x) = 2x – 1,P2(x) = x² + 3x – 1, p3(x) = 1- 2x + x*} Note: You will have to solve c1P1(x) + c2P2(x)+c3P3(x) here are several ways to do this. You could plug in points to get equations in the c's. Or you an expand and equate coefficients. Or you could differentiate both sides of the equation. = 0 for the c's.
4. Determine whether or not the following functions are linearly independent in the vector space P4. {p:(x) = 2x – 1,P2(x) = x² + 3x – 1, p3(x) = 1- 2x + x*} Note: You will have to solve c1P1(x) + c2P2(x)+c3P3(x) here are several ways to do this. You could plug in points to get equations in the c's. Or you an expand and equate coefficients. Or you could differentiate both sides of the equation. = 0 for the c's.
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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![4. Determine whether or not the following functions are linearly independent in the vector
space P4.
{p,(x) = 2x – 1, p2(x) = x² + 3x – 1,p3(x) =
1- 2x + x*}
Note: You will have to solve c¡P;(x) + C2P2 (x)+C3P3(x)
There are several ways to do this. You could plug in points to get equations in the c's. Or you
can expand and equate coefficients. Or you could differentiate both sides of the equation.
= 0 for the c's.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaffebe2-b28f-432c-a7fc-3f771511d49f%2F3ccfd9cb-6c45-4e44-8ee2-cec4433b17b8%2Ftdzuu4_processed.png&w=3840&q=75)
Transcribed Image Text:4. Determine whether or not the following functions are linearly independent in the vector
space P4.
{p,(x) = 2x – 1, p2(x) = x² + 3x – 1,p3(x) =
1- 2x + x*}
Note: You will have to solve c¡P;(x) + C2P2 (x)+C3P3(x)
There are several ways to do this. You could plug in points to get equations in the c's. Or you
can expand and equate coefficients. Or you could differentiate both sides of the equation.
= 0 for the c's.
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