Show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X₂, ... are not vectors but are entries in vectors. T(X1 X2 X3) = (x₁ - 8x2 +5X3, X2-9X3) A = =(Type an integer or decimal for each matrix element.) .....
Show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X₂, ... are not vectors but are entries in vectors. T(X1 X2 X3) = (x₁ - 8x2 +5X3, X2-9X3) A = =(Type an integer or decimal for each matrix element.) .....
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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![**Linear Transformation and Matrix Representation**
To demonstrate that \( T \) is a linear transformation, we need to find a matrix that implements the mapping.
**Mapping Definition:**
Given:
\[ T(x_1, x_2, x_3) = (x_1 - 8x_2 + 5x_3, \, x_2 - 9x_3) \]
**Matrix Representation:**
We are tasked with finding matrix \( A \) such that:
\[ A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \]
### Instructions:
- Enter an integer or decimal for each matrix element.
The matrix \( A \) will map a vector \((x_1, x_2, x_3)\) through the transformation \( T \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ec5dee8-4b81-4c1e-b6ca-023c2626018b%2Ff9f37036-ead7-4719-871d-da86ebb9ef89%2Fha8qwcq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Linear Transformation and Matrix Representation**
To demonstrate that \( T \) is a linear transformation, we need to find a matrix that implements the mapping.
**Mapping Definition:**
Given:
\[ T(x_1, x_2, x_3) = (x_1 - 8x_2 + 5x_3, \, x_2 - 9x_3) \]
**Matrix Representation:**
We are tasked with finding matrix \( A \) such that:
\[ A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \]
### Instructions:
- Enter an integer or decimal for each matrix element.
The matrix \( A \) will map a vector \((x_1, x_2, x_3)\) through the transformation \( T \).
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