Define T:P2→R as shown to the right. p(- 1) a. Find the image under T of p(t) = 4 - 3t. T(p) = p(0) b. Show that T is a linear transformation. P(3) c. Find the matrix for T relative to the basis B= (b, , b2, b3} = {1, t, t?} for P, and the standard basis E= (e,, e,, ez} for R a. The image under T of p(t) = 4- 3t is

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Define T:P2→R as shown to the right.
p(- 1)
a. Find the image under T of p(t) = 4 - 3t.
T(p) =
p(0)
b. Show that T is a linear transformation.
P(3)
c. Find the matrix for T relative to the basis B= (b, , b2, b3} = {1, t, t?} for P, and the standard basis E= (e,, e,, ez} for R
a. The image under T of p(t) = 4- 3t is
Transcribed Image Text:Define T:P2→R as shown to the right. p(- 1) a. Find the image under T of p(t) = 4 - 3t. T(p) = p(0) b. Show that T is a linear transformation. P(3) c. Find the matrix for T relative to the basis B= (b, , b2, b3} = {1, t, t?} for P, and the standard basis E= (e,, e,, ez} for R a. The image under T of p(t) = 4- 3t is
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