
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.](https://content.bartleby.com/qna-images/question/a824ef54-0ee2-4591-9058-ff8a94975446/828655d6-eaf4-4ba9-a65e-11b93fd6a981/40o5omd_thumbnail.jpeg)
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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