)Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let Pi (z) P2(1) = 2-z+z-', 6-3z + 3z- 3r, 2+2-r, Ps (2) PA(z) - 3-z+ 2z- 2r and let C = {pi (2), P2 (2), Pa (2), P4(#)}. a. Use coordinate representations with respect to the basis B = {1, r,r,r} to determine whether the set C forms a basis for Pa. choose b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials. } C. The dimension of span(C) is
)Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let Pi (z) P2(1) = 2-z+z-', 6-3z + 3z- 3r, 2+2-r, Ps (2) PA(z) - 3-z+ 2z- 2r and let C = {pi (2), P2 (2), Pa (2), P4(#)}. a. Use coordinate representations with respect to the basis B = {1, r,r,r} to determine whether the set C forms a basis for Pa. choose b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials. } C. The dimension of span(C) is
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 P3 be the vector space of all polynomials of degree 3 or less in the variable r. Let
P1 (x)
P2 (1)
P3 (x)
2-z+ z? - r,
3z + 3z2-3r,
2+ z-z',
- 2r3
6.
PA (x) =
3-z+ 2z?
and let C = {p1 (x), P2 (æ), P3 (2), P4 (x)}.
choose
a. Use coordinate representations with respect to the basis B {1, r, r-,r'} to determine whether the set C forms a basis for Pg.
b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials.
{
}
c. The dimension of span(C) is
S07 PM](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0afc3b-3e57-4487-b673-cf6f07e8890b%2Fbfd69cbc-7525-4b66-bbec-52181fe1c183%2Fo1dmrmr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:}) Let P3 be the vector space of all polynomials of degree 3 or less in the variable r. Let
P1 (x)
P2 (1)
P3 (x)
2-z+ z? - r,
3z + 3z2-3r,
2+ z-z',
- 2r3
6.
PA (x) =
3-z+ 2z?
and let C = {p1 (x), P2 (æ), P3 (2), P4 (x)}.
choose
a. Use coordinate representations with respect to the basis B {1, r, r-,r'} to determine whether the set C forms a basis for Pg.
b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials.
{
}
c. The dimension of span(C) is
S07 PM
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