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Let L be a linear transformation from P₂ → R2x2 such that L(f) — ƒ(1) 0 Find dim[Range(L)] ƒ(2) [ƒ(2) ƒ(0)

Let L be a linear transformation from P₂ → R2x2 such that L(f) — ƒ(1) 0 Find dim[Range(L)] ƒ(2) [ƒ(2) ƒ(0)

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 \( L \) be a linear transformation from \( P_2 \rightarrow \mathbb{R}^{2 \times 2} \) such that \[ L(f) := \begin{bmatrix} f(2) - f(1) & 0 \\ 0 & f(0) \end{bmatrix} \] Find \(\text{dim}[\text{Range}(L)]\).
Transcribed Image Text:Let \( L \) be a linear transformation from \( P_2 \rightarrow \mathbb{R}^{2 \times 2} \) such that \[ L(f) := \begin{bmatrix} f(2) - f(1) & 0 \\ 0 & f(0) \end{bmatrix} \] Find \(\text{dim}[\text{Range}(L)]\).
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