Let T : P₂ → R² be a linear transformation defined by T(p) = [(0)]. O {ait a₁ € R} O {azt²a2 € R} O fait + a2t² lai, a2 € R} O fait + azt² la₁ + a₂ = 0} O P₂2 Find the kernel of T.
Let T : P₂ → R² be a linear transformation defined by T(p) = [(0)]. O {ait a₁ € R} O {azt²a2 € R} O fait + a2t² lai, a2 € R} O fait + azt² la₁ + a₂ = 0} O P₂2 Find the kernel of T.
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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Transcribed Image Text:The image presents a mathematical problem involving a linear transformation. Here is the transcription:
"Let \( T : P_2 \rightarrow \mathbb{R}^2 \) be a linear transformation defined by \( T(p) = \begin{bmatrix} p(0) \\ p(0) \end{bmatrix} \). Find the kernel of \( T \).
Options:
- \( \{ a_1 t \mid a_1 \in \mathbb{R} \} \)
- \( \{ a_2 t^2 \mid a_2 \in \mathbb{R} \} \)
- \( \{ a_1 + a_2 t^2 \mid a_1, a_2 \in \mathbb{R} \} \)
- \( \{ a_1 + a_2 t^2 \mid a_1 + a_2 = 0 \} \)
- \( P_2 \)
A hand partially obscures the image."
No graphs or diagrams are present.
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