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Let T : P2(R) → M2×2 (R) be the linear transformation defined by T (f(x)) = ($(0) 0 f(5) f(4 - ° ƒ (4). Let ẞ = {1,x,x²} be the standard basis for P₂(R). Find bases for both the range R(T) and the null space N(T), and verify the dimension theorem.

Let T : P2(R) → M2×2 (R) be the linear transformation defined by T (f(x)) = ($(0) 0 f(5) f(4 - ° ƒ (4). Let ẞ = {1,x,x²} be the standard basis for P₂(R). Find bases for both the range R(T) and the null space N(T), and verify the dimension theorem.

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 P₂(R) → M2×2(R) be the linear transformation defined by T (f(x)) = (ƒ(0) 0 f(5) - – ° ƒ(4)). Let ẞ= {1, x, x²} be the standard basis for P₂(R). Find bases for both the range R(T) and the null space N(T), and verify the dimension theorem.
Transcribed Image Text:Let T P₂(R) → M2×2(R) be the linear transformation defined by T (f(x)) = (ƒ(0) 0 f(5) - – ° ƒ(4)). Let ẞ= {1, x, x²} be the standard basis for P₂(R). Find bases for both the range R(T) and the null space N(T), and verify the dimension theorem.
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