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3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as appropriate. (a) T : M2,2 → R defined by T ( :) = ad – bc. d (b) S: P2 → P3 defined by S(p(x)) = xp(x) + P(x). (c) In the case of S, calculate the standard matrix representation.

3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as appropriate. (a) T : M2,2 → R defined by T ( :) = ad – bc. d (b) S: P2 → P3 defined by S(p(x)) = xp(x) + P(x). (c) In the case of S, calculate the standard matrix representation.

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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3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as appropriate. a b (a) T: M2,2 → R defined by T = ad – bc. d (b) S: P2 → P3 defined by S(p(x)) = xp(x) + p(x). (c) In the case of S, calculate the standard matrix representation.
Transcribed Image Text:3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as appropriate. a b (a) T: M2,2 → R defined by T = ad – bc. d (b) S: P2 → P3 defined by S(p(x)) = xp(x) + p(x). (c) In the case of S, calculate the standard matrix representation.
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