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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### 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 ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532cb823-0c19-4b15-a905-a7d232958517%2F840b31ab-f28d-455d-9468-131937ea2a3c%2Fq1txlb_processed.jpeg&w=3840&q=75)
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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