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Let T: P2 → P, be the linear transformation such that T(2x) = 2x2 – 3x, T(0.5x – 4) = -2x² – 4x + 3, T(4x² + 1) = -4x + 4. Find T(1), T(x), T(x²), and T(ax2 + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =

Let T: P2 → P, be the linear transformation such that T(2x) = 2x2 – 3x, T(0.5x – 4) = -2x² – 4x + 3, T(4x² + 1) = -4x + 4. Find T(1), T(x), T(x²), and T(ax2 + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =

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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Let T : P2 → P, be the linear transformation such that T(2x) = 2x? – 3x, T(0.5x – 4) = -2x – 4x + 3, T(4x² + 1) = –4x + 4. %3D Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =
Transcribed Image Text:Let T : P2 → P, be the linear transformation such that T(2x) = 2x? – 3x, T(0.5x – 4) = -2x – 4x + 3, T(4x² + 1) = –4x + 4. %3D Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =
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