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5. Let T: P₂ (R) → P₂ (R) be defined as P(ax² +bx+c)=((2a − b)x² + (3a + 3c)x+ (a − 2b - 3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism, find the inverse of T.

5. Let T: P₂ (R) → P₂ (R) be defined as P(ax² +bx+c)=((2a − b)x² + (3a + 3c)x+ (a − 2b - 3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism, find the inverse 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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solve #5 please, Show all of your work on pictures and explain each step you make.

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5. Let T: P₂ (R) → P₂(R) be defined as P(ax² +bx+c)=( (2a − b)x² + (3a + 3c)x + (a − 2b - 3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism, find the inverse of T. 6. Let
Transcribed Image Text:5. Let T: P₂ (R) → P₂(R) be defined as P(ax² +bx+c)=( (2a − b)x² + (3a + 3c)x + (a − 2b - 3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism, find the inverse of T. 6. Let
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