4 and define T : R²→R2 by T(x) = Ax. Find the images under T of u = - 3 4 0 a and v = b Let A = 0 4 ..... T(u) =
4 and define T : R²→R2 by T(x) = Ax. Find the images under T of u = - 3 4 0 a and v = b Let A = 0 4 ..... T(u) =
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
![Let \( A = \begin{bmatrix} 4 & 0 \\ 0 & 4 \end{bmatrix} \), and define \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) by \( T(\mathbf{x}) = A\mathbf{x} \). Find the images under \( T \) of \( \mathbf{u} = \begin{bmatrix} 4 \\ -3 \end{bmatrix} \) and \( \mathbf{v} = \begin{bmatrix} a \\ b \end{bmatrix} \).
\[ T(\mathbf{u}) = \boxed{\phantom{\text{answer}}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F704a64b5-5250-41d0-9c29-5aaf5a50e535%2F884a17b9-4fee-4a7d-8b62-465df07c9cf1%2Fc2regmp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( A = \begin{bmatrix} 4 & 0 \\ 0 & 4 \end{bmatrix} \), and define \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) by \( T(\mathbf{x}) = A\mathbf{x} \). Find the images under \( T \) of \( \mathbf{u} = \begin{bmatrix} 4 \\ -3 \end{bmatrix} \) and \( \mathbf{v} = \begin{bmatrix} a \\ b \end{bmatrix} \).
\[ T(\mathbf{u}) = \boxed{\phantom{\text{answer}}} \]
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