Problem 8. Determine which of the following are linear maps. Prove your answers. (a) T₁ : R² → R2 defined by T(x, y) = (2x − y, x+y). (b) T₂: R² → R² defined by T(x, y) = (0, xy). (c) T3 : P(R) → R defined by T3(p) = |p'(0)|. (d) T₁ : R³ → P2 (R) defined by [T₁(a, b, c)](x) = a +bx+cx² for all x E R.
Problem 8. Determine which of the following are linear maps. Prove your answers. (a) T₁ : R² → R2 defined by T(x, y) = (2x − y, x+y). (b) T₂: R² → R² defined by T(x, y) = (0, xy). (c) T3 : P(R) → R defined by T3(p) = |p'(0)|. (d) T₁ : R³ → P2 (R) defined by [T₁(a, b, c)](x) = a +bx+cx² for all x E R.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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 = a + bx + cx²
for all x ER.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F979d0aba-5428-414f-a3ba-5510f0301082%2Fb7064f36-46b0-4e13-b3f7-68b92521e142%2Fmm310mq_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 8. Determine which of the following are linear maps. Prove your answers.
2
(a) T₁ R² R2 defined by T(x, y) = (2x - y, x + y).
:
(b) T₂ : R² → R² defined by T(x, y) = (0, xy).
(c) T3: P(R) → R defined by T3(p) = [p'(0)|.
(d) T₁ : R³ → P2 (R) defined by
[T₁(a, b, c)](x) = a + bx + cx²
for all x ER.
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