Define T: R² → R² by T(x) = Ax. Find a basis B for R² with the property that [T] is diagonal. -=[₁ A= 2-7 -5 4 A basis for R² with the property that [T] is diagonal is. (Type a vector or list of vectors. Use a comma to separate vectors as needed.)
Define T: R² → R² by T(x) = Ax. Find a basis B for R² with the property that [T] is diagonal. -=[₁ A= 2-7 -5 4 A basis for R² with the property that [T] is diagonal is. (Type a vector or list of vectors. Use a comma to separate vectors as needed.)
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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![Define \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) by \( T(\mathbf{x}) = A\mathbf{x} \). Find a basis \( B \) for \( \mathbb{R}^2 \) with the property that \([T]_B\) is diagonal.
\[
A = \begin{bmatrix} 2 & -7 \\ -5 & 4 \end{bmatrix}
\]
---
A basis for \( \mathbb{R}^2 \) with the property that \([T]_B\) is diagonal is \(\boxed{\phantom{1}}\).
(Type a vector or list of vectors. Use a comma to separate vectors as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46029127-96a5-4dc2-997a-3c090d1aab2d%2F6ef4ba2c-b44f-4581-805c-7598998efe34%2Fsuditj9_processed.png&w=3840&q=75)
Transcribed Image Text:Define \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) by \( T(\mathbf{x}) = A\mathbf{x} \). Find a basis \( B \) for \( \mathbb{R}^2 \) with the property that \([T]_B\) is diagonal.
\[
A = \begin{bmatrix} 2 & -7 \\ -5 & 4 \end{bmatrix}
\]
---
A basis for \( \mathbb{R}^2 \) with the property that \([T]_B\) is diagonal is \(\boxed{\phantom{1}}\).
(Type a vector or list of vectors. Use a comma to separate vectors as needed.)
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