Let T be the linear transformation from the space of degree three or less polynomials to itself defined by the following formula: T(ax³ + bx² + cx + d) = (a − b)x³ + (a - b)x² + (2c+ d)x + (2c+ d) T. Find a basis for the image of

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 15CR
Question
Let T be the linear transformation from the space of degree three or less polynomials
to itself defined by the following formula:
T(ax³ + bx² + cx + d) = (a − b)x³ + (a - b)x² + (2c+ d)x + (2c+ d)
T.
Find a basis for the image of
Transcribed Image Text:Let T be the linear transformation from the space of degree three or less polynomials to itself defined by the following formula: T(ax³ + bx² + cx + d) = (a − b)x³ + (a - b)x² + (2c+ d)x + (2c+ d) T. Find a basis for the image of
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