T 8-1 H = 2 1 & T = 6 5 Find T TB] (NO guess and check on linear combinations!)
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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Question
![The problem presents a transformation \( T \) applied on vectors. We have the following given transformations:
\[
T \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}
\]
and
\[
T \begin{bmatrix} 3 \\ 4 \end{bmatrix} = \begin{bmatrix} -3 \\ 6 \\ 5 \end{bmatrix}
\]
You are tasked to find:
\[
T \begin{bmatrix} 3 \\ 5 \end{bmatrix}
\]
The instruction indicates not to use guess and check for linear combinations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2b7ff9-b952-4215-9e0f-f264e2036fb8%2F5cf56344-e3e2-4366-a640-0e2e4a9148c7%2F4j0rkqs_processed.png&w=3840&q=75)
Transcribed Image Text:The problem presents a transformation \( T \) applied on vectors. We have the following given transformations:
\[
T \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}
\]
and
\[
T \begin{bmatrix} 3 \\ 4 \end{bmatrix} = \begin{bmatrix} -3 \\ 6 \\ 5 \end{bmatrix}
\]
You are tasked to find:
\[
T \begin{bmatrix} 3 \\ 5 \end{bmatrix}
\]
The instruction indicates not to use guess and check for linear combinations.
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