Let T: P2(R) → P3(R) be a linear transformation given by T(F(x)) = 2f'(x)+integral with (lower bound 0 and upper bound x) 3f(t)dt. Is T one-to-one? Is T onto?
Let T: P2(R) → P3(R) be a linear transformation given by T(F(x)) = 2f'(x)+integral with (lower bound 0 and upper bound x) 3f(t)dt. Is T one-to-one? Is T onto?
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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Defn.: A function T: V→W is one-to-one (injective) if T(x1)=T(x2) implies x1=x2. T is onto (surjective) if T(V)=W.
Let T: P2(R) → P3(R) be a linear transformation given by T(F(x)) = 2f'(x)+integral with (lower bound 0 and upper bound x) 3f(t)dt.
Is T one-to-one? Is T onto? Provide prove for both.
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