Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the standard basis for P2; ß the basis consisting of x² + 3x, x² – 2, x + 6; v= 4x² + 5x – 2. %3D (a) Find [T]% where a is the standard basis for P,. (b) Find the change of basis matrix from a to ß. (c) Find the change of basis matrix from ß to a. (d) Find [T]. (e) Find [v]g. (1) Find [T(v)]g- (g) Find T(v).
Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the standard basis for P2; ß the basis consisting of x² + 3x, x² – 2, x + 6; v= 4x² + 5x – 2. %3D (a) Find [T]% where a is the standard basis for P,. (b) Find the change of basis matrix from a to ß. (c) Find the change of basis matrix from ß to a. (d) Find [T]. (e) Find [v]g. (1) Find [T(v)]g- (g) Find T(v).
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 T: P2 → P2 by
T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c);
a the standard basis for P2; ß the basis consisting of
x² + 3x, x² – 2, x + 6; v= 4x² + 5x – 2.
(a) Find [T]% where a is the standard basis for P,.
(b) Find the change of basis matrix from a to ß.
(c) Find the change of basis matrix from ß to a.
(d) Find [T].
(e) Find [v]g.
(1) Find [T(v)]g -
(g) Find T(v).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85ff80cd-34a8-4471-9907-d9de1b52412a%2F6b620376-2a0b-4104-8e53-ec9189eaf29b%2Fo1pjo1w_processed.png&w=3840&q=75)
Transcribed Image Text:Let T: P2 → P2 by
T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c);
a the standard basis for P2; ß the basis consisting of
x² + 3x, x² – 2, x + 6; v= 4x² + 5x – 2.
(a) Find [T]% where a is the standard basis for P,.
(b) Find the change of basis matrix from a to ß.
(c) Find the change of basis matrix from ß to a.
(d) Find [T].
(e) Find [v]g.
(1) Find [T(v)]g -
(g) Find T(v).
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