
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:The image contains handwritten equations exploring whether two functions, S and T, commute. The question posed is: "Do S and T commute?"
Here are the definitions of the functions:
1. **Function S**:
- \( S(x, y, z) = (3x, 3y, 3z) \)
- This function scales each component of the input vector \((x, y, z)\) by 3.
2. **Function T**:
- \( T(x, y, z) = (x, y) \)
- This function projects the input vector \((x, y, z)\) onto the xy-plane, effectively eliminating the z-component.
To determine if S and T commute, we would need to check if applying S and then T yields the same result as applying T and then S, given the same input. In other words, if \( T(S(x, y, z)) = S(T(x, y, z)) \) for all input vectors \((x, y, z)\).
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