Define ime a function T: P3 → P3 and π(p(t)) = + pl(t). a. Prove T is a linear transformation ansider the following two bases for P3 B = { 1, 1, 1², 13] Now and C= {2, 2-1, 5-4+++², 61² + 3 + +3+³7 Show that C is a basis for P3 c. Find the matrix for T relative to the basis B for the domain and the basis C for the codomain. Solve systems of equations found in in the d. Let M denote the matrix you previous part. Use M to easily find the C-ecordinates of T (17 +++ t²_1³) You Should not use the original formula for T and do not solve anys system of equations,
Define ime a function T: P3 → P3 and π(p(t)) = + pl(t). a. Prove T is a linear transformation ansider the following two bases for P3 B = { 1, 1, 1², 13] Now and C= {2, 2-1, 5-4+++², 61² + 3 + +3+³7 Show that C is a basis for P3 c. Find the matrix for T relative to the basis B for the domain and the basis C for the codomain. Solve systems of equations found in in the d. Let M denote the matrix you previous part. Use M to easily find the C-ecordinates of T (17 +++ t²_1³) You Should not use the original formula for T and do not solve anys system of equations,
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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Question
![r.
Define a function T: P3 → P3 and TC p(t)) = tp²(t).
a. Prove T is a linear transformation
Now consider the following two bases for P3
B=
= { 1, 1, 1², 13]
and C= {2, 2-1, 5-4+ +1²³, 61³²+ 3+³ ]
31
V
Show that C is a basis for
Find the matrix for T relative to the basis B for the domain
for the codomain. Solve systems of equations
found in
d. Let M denote the matrix
the
you
previous part.
lise M to easily find the C-ecordinates of T(17+ + + +²_1³) You
Should not use the original formula for T and do not solve any
system of aquations.
Ca
and the basis C for
P3
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Transcribed Image Text:r.
Define a function T: P3 → P3 and TC p(t)) = tp²(t).
a. Prove T is a linear transformation
Now consider the following two bases for P3
B=
= { 1, 1, 1², 13]
and C= {2, 2-1, 5-4+ +1²³, 61³²+ 3+³ ]
31
V
Show that C is a basis for
Find the matrix for T relative to the basis B for the domain
for the codomain. Solve systems of equations
found in
d. Let M denote the matrix
the
you
previous part.
lise M to easily find the C-ecordinates of T(17+ + + +²_1³) You
Should not use the original formula for T and do not solve any
system of aquations.
Ca
and the basis C for
P3
CS Scanned with CamScanner
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