Define T:R³ R³ by T → Then we can write T(7) - D-[ Az where A- I1 - 23 11 + 312 - 13 12 +213
Define T:R³ R³ by T → Then we can write T(7) - D-[ Az where A- I1 - 23 11 + 312 - 13 12 +213
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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Refer to image below to find 3 *3 matrix
![**Defining the Linear Transformation:**
The transformation \( T: \mathbb{R}^3 \to \mathbb{R}^3 \) is defined by:
\[
T \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{bmatrix} x_1 - x_3 \\ x_1 + 3x_2 - x_3 \\ x_2 + 2x_3 \end{bmatrix}
\]
**Matrix Representation:**
This transformation can be expressed as a matrix multiplication \( T(\mathbf{x}) = A\mathbf{x} \) where \( A \) is the matrix that represents the transformation in the standard basis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F181283bb-83dc-4f09-86f1-fac04e6d4723%2F24d96bb5-c948-4e2b-9367-07843ad24296%2Fub78bwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Defining the Linear Transformation:**
The transformation \( T: \mathbb{R}^3 \to \mathbb{R}^3 \) is defined by:
\[
T \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{bmatrix} x_1 - x_3 \\ x_1 + 3x_2 - x_3 \\ x_2 + 2x_3 \end{bmatrix}
\]
**Matrix Representation:**
This transformation can be expressed as a matrix multiplication \( T(\mathbf{x}) = A\mathbf{x} \) where \( A \) is the matrix that represents the transformation in the standard basis.
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