T: P2 P2, T(ax2 + bx + c) = ax² + bx + c B = {1, 1 – x, (1 – x)²} B' = {1, x, x²} %3D - 6. v = x² – 3x + 3

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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T: V ---> V is a linear operator with a B and B' ordered bases for V

a. Find the matrix representation for T relative to the ordered bases B and B'

b. Find T(v), using a direct computation and using the matrix representation

9. T: P2 P2,
T(ax2 + bx + c) = ax+ bx +c
B = {1, 1 – x, (1 – x)²}
%3D
B' = {1, x, x²}
v = x² – 3x + 3
-
Transcribed Image Text:9. T: P2 P2, T(ax2 + bx + c) = ax+ bx +c B = {1, 1 – x, (1 – x)²} %3D B' = {1, x, x²} v = x² – 3x + 3 -
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