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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.

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.

Advanced Engineering Mathematics
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 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.
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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