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Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(f(t)) = f(6) from Pg to R B. T(f(t)) = f'(t) +9f(t) + 5 from C∞ to C∞ c. T(f(t)) = f(t)f' (t) from P4 to P₁ D. T(x + y) = 7xiy from C to C E. T(f(t)) = t'f' (t) from P₂ to P8 L -4 F. T(f(t)) = f(t)dt from P5 to R

Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(f(t)) = f(6) from Pg to R B. T(f(t)) = f'(t) +9f(t) + 5 from C∞ to C∞ c. T(f(t)) = f(t)f' (t) from P4 to P₁ D. T(x + y) = 7xiy from C to C E. T(f(t)) = t'f' (t) from P₂ to P8 L -4 F. T(f(t)) = f(t)dt from P5 to R

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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Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. □A. T(f(t)) = f(6) from Pg to R |B. T(f(t)) = ƒ' (t) + 9f (t) + 5 from Co to Co c. T(fƒ(t)) = f(t)ƒ' (t) from P4 to P₁ D. T(x + y) = 7x - iy from C to C ✔ɛ. T(f(t)) = t¹ƒ' (t) from P₂ to Pg 9 ✔ = L -4 F. T(f(t)) f(t)dt from P5 to R
Transcribed Image Text:Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. □A. T(f(t)) = f(6) from Pg to R |B. T(f(t)) = ƒ' (t) + 9f (t) + 5 from Co to Co c. T(fƒ(t)) = f(t)ƒ' (t) from P4 to P₁ D. T(x + y) = 7x - iy from C to C ✔ɛ. T(f(t)) = t¹ƒ' (t) from P₂ to Pg 9 ✔ = L -4 F. T(f(t)) f(t)dt from P5 to R
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