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What matrix would the translate by [1, 2, 3] be? 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 2 3 1 0 0 0 1 0 0 0 1 0 2 3 0 0 1 0 0 0 0 2 0 0 0030 0 0 0 0

What matrix would the translate by [1, 2, 3] be? 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 2 3 1 0 0 0 1 0 0 0 1 0 2 3 0 0 1 0 0 0 0 2 0 0 0030 0 0 0 0

Advanced Engineering Mathematics
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 What matrix would translate by [1, 2, 3] be? ### Options 1. ``` [ 1 0 0 0 ] [ 0 2 0 0 ] [ 0 0 3 0 ] [ 0 0 0 1 ] ``` 2. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 1 2 3 1 ] ``` 3. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 1 2 3 0 ] ``` 4. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 2 0 0 ] [ 0 0 3 0 ] ``` ### Explanation The goal is to determine which matrix corresponds to a translation transformation by the vector [1, 2, 3] in a 3D space. The translation matrix takes the form: ``` [ 1 0 0 Tx ] [ 0 1 0 Ty ] [ 0 0 1 Tz ] [ 0 0 0 1 ] ``` Where Tx, Ty, Tz are the translation components in the x, y, and z directions, respectively. Therefore, the correct matrix that translates by [1, 2, 3] is: ``` [ 1 0 0 1 ] [ 0 1 0 2 ] [ 0 0 1 3 ] [ 0 0 0 1 ] ``` Thus, the correct option is the second one with an adjusted fourth row to `[ 0 0 0 1 ]
Transcribed Image Text:### Question What matrix would translate by [1, 2, 3] be? ### Options 1. ``` [ 1 0 0 0 ] [ 0 2 0 0 ] [ 0 0 3 0 ] [ 0 0 0 1 ] ``` 2. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 1 2 3 1 ] ``` 3. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 1 2 3 0 ] ``` 4. ``` [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 2 0 0 ] [ 0 0 3 0 ] ``` ### Explanation The goal is to determine which matrix corresponds to a translation transformation by the vector [1, 2, 3] in a 3D space. The translation matrix takes the form: ``` [ 1 0 0 Tx ] [ 0 1 0 Ty ] [ 0 0 1 Tz ] [ 0 0 0 1 ] ``` Where Tx, Ty, Tz are the translation components in the x, y, and z directions, respectively. Therefore, the correct matrix that translates by [1, 2, 3] is: ``` [ 1 0 0 1 ] [ 0 1 0 2 ] [ 0 0 1 3 ] [ 0 0 0 1 ] ``` Thus, the correct option is the second one with an adjusted fourth row to `[ 0 0 0 1 ]
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