Suppose that T : R² → R² is a linear transformation and that T ([]) = [] (B³]) Find the standard matrix for T, that is, the matrix A such that T (1-¹)) = 6] T(v) Av for any v E R². = and
Suppose that T : R² → R² is a linear transformation and that T ([]) = [] (B³]) Find the standard matrix for T, that is, the matrix A such that T (1-¹)) = 6] T(v) Av for any v E R². = and
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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![Suppose that \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) is a linear transformation and that
\[
T \left( \begin{bmatrix} 2 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 1 \\ 3 \end{bmatrix}
\]
and
\[
T \left( \begin{bmatrix} 1 \\ -1 \end{bmatrix} \right) = \begin{bmatrix} 0 \\ 5 \end{bmatrix}.
\]
Find the standard matrix for \( T \), that is, the matrix \( A \) such that \( T(\vec{v}) = A\vec{v} \) for any \( \vec{v} \in \mathbb{R}^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe00cebfb-aec4-474d-8979-79a2d105b819%2F81cb8402-eb3f-436e-92dd-06291d22eab7%2F9sf4vcg_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) is a linear transformation and that
\[
T \left( \begin{bmatrix} 2 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 1 \\ 3 \end{bmatrix}
\]
and
\[
T \left( \begin{bmatrix} 1 \\ -1 \end{bmatrix} \right) = \begin{bmatrix} 0 \\ 5 \end{bmatrix}.
\]
Find the standard matrix for \( T \), that is, the matrix \( A \) such that \( T(\vec{v}) = A\vec{v} \) for any \( \vec{v} \in \mathbb{R}^2 \).
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