Let T be the linear transformation from the space of degree three or less polynomials to itself defined by the following formula: T(ax + bx²+cx+ d) = (a - b)x³ + (a - b)x² + (2c+ d)x+(2c+d) Find a basis for the null space of T.
Let T be the linear transformation from the space of degree three or less polynomials to itself defined by the following formula: T(ax + bx²+cx+ d) = (a - b)x³ + (a - b)x² + (2c+ d)x+(2c+d) Find a basis for the null space of T.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 56RE
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![Let T be the linear transformation from the space of degree three or less polynomials
to itself defined by the following formula:
T(ax + bx²+cx+ d) = (a - b)x³ + (a - b)x² + (2c+ d)x+(2c+d)
Find a basis for the null space of T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34cc5c6b-5450-4c98-93f3-d37eba173724%2F6b09eb39-b584-4d13-9922-1fc9bd2f4332%2F2hwycjr_processed.png&w=3840&q=75)
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(ax + bx²+cx+ d) = (a - b)x³ + (a - b)x² + (2c+ d)x+(2c+d)
Find a basis for the null space of T.
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