Does this equation define a linear transformation from R3 to R2?
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
Does this equation define a linear transformation from R3 to R2?
![The image contains a mathematical transformation notation and reads:
\[ T(x, y, z) = (x+5, y+5) \]
**Explanation:**
This expression represents a transformation function \( T \) that takes a point in three-dimensional space with coordinates \( (x, y, z) \) and maps it to a new point in two-dimensional space with coordinates \( (x+5, y+5) \).
- **Input**: The original coordinates are given as \( (x, y, z) \).
- **Transformation**:
- The x-coordinate of the new point is calculated by adding 5 to the original x-coordinate.
- The y-coordinate of the new point is calculated by adding 5 to the original y-coordinate.
Note: The z-coordinate is not altered in this transformation and does not appear in the output, indicating a dimensional reduction from 3D to 2D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa824ef54-0ee2-4591-9058-ff8a94975446%2F828655d6-eaf4-4ba9-a65e-11b93fd6a981%2F40o5omd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical transformation notation and reads:
\[ T(x, y, z) = (x+5, y+5) \]
**Explanation:**
This expression represents a transformation function \( T \) that takes a point in three-dimensional space with coordinates \( (x, y, z) \) and maps it to a new point in two-dimensional space with coordinates \( (x+5, y+5) \).
- **Input**: The original coordinates are given as \( (x, y, z) \).
- **Transformation**:
- The x-coordinate of the new point is calculated by adding 5 to the original x-coordinate.
- The y-coordinate of the new point is calculated by adding 5 to the original y-coordinate.
Note: The z-coordinate is not altered in this transformation and does not appear in the output, indicating a dimensional reduction from 3D to 2D.
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