). -b 41. Define G : P2 –→ M2x2 by G(ax² + bx +e) = ( | a 0 с+3а (a) What is the image of 3r? + 2r – 1 under G? (b) Prove/Justify whether or not G is a linear transformation using the definition of linear transformation. (c) If G is a linear transformation. Find a matrix representation of it.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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a
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41. Define G : P2 → M2x2 by G(ax² + bæ + c) = (
0 c+ 3a
(a) What is the image of 3x? + 2a
1 under G?
(b) Prove/Justify whether or not G is a linear transformation using the definition of linear
transformation.
(c) If G is a linear transformation. Find a matrix representation of it.
Transcribed Image Text::). a -b 41. Define G : P2 → M2x2 by G(ax² + bæ + c) = ( 0 c+ 3a (a) What is the image of 3x? + 2a 1 under G? (b) Prove/Justify whether or not G is a linear transformation using the definition of linear transformation. (c) If G is a linear transformation. Find a matrix representation of it.
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