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Let T: P₁ → R² be defined by T (P) Let q(t) = 5t6t² +7t³. Find T(q). Find a basis for the kernel of T. where p'(t) is the derivative of the arbitrary polynomial p(t) = a + a₁t+ a₂t² + ast³ + astª, where ao, a1, 92, 93, 94 € R. Find a basis for the range of T. - p(0) p'(0)

Let T: P₁ → R² be defined by T (P) Let q(t) = 5t6t² +7t³. Find T(q). Find a basis for the kernel of T. where p'(t) is the derivative of the arbitrary polynomial p(t) = a + a₁t+ a₂t² + ast³ + astª, where ao, a1, 92, 93, 94 € R. Find a basis for the range of T. - p(0) p'(0)

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: P₁ → R² be defined by T (P) Let q(t) = 5t6t² +7t³. Find T(q). Find a basis for the kernel of T. where p'(t) is the derivative of the arbitrary polynomial p(t) = a + a₁t+ a₂t² + ast³ + astª, where ao, a1, 92, 93, 94 € R. Find a basis for the range of T. - p(0) p'(0)
Transcribed Image Text:Let T: P₁ → R² be defined by T (P) Let q(t) = 5t6t² +7t³. Find T(q). Find a basis for the kernel of T. where p'(t) is the derivative of the arbitrary polynomial p(t) = a + a₁t+ a₂t² + ast³ + astª, where ao, a1, 92, 93, 94 € R. Find a basis for the range of T. - p(0) p'(0)
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