What would the image of (1, 2, 3) be under the transformation modeled by 1000 0 1 0 0 0010 1 2 3 1 ? O (1,2,3) (1,4,9) (2, 4, 6) (0,0,0)
What would the image of (1, 2, 3) be under the transformation modeled by 1000 0 1 0 0 0010 1 2 3 1 ? O (1,2,3) (1,4,9) (2, 4, 6) (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
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![### Matrix Transformation Question
#### Problem Statement
What would the image of the vector \( (1, 2, 3) \) be under the transformation modeled by the following matrix?
\[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 2 & 3 & 1
\end{bmatrix}
\]
#### Options
- O (1, 2, 3)
- O (1, 4, 9)
- O (2, 4, 6)
- O (0, 0, 0)
This exercise involves applying a matrix transformation to a 3D vector in homogeneous coordinates. The matrix given is a 4x4 transformation matrix, often used in 3D graphics and computational geometry. The problem is designed to test understanding of matrix-vector multiplication and transformation applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532cb823-0c19-4b15-a905-a7d232958517%2Fa5155b2b-1736-419b-b713-9f9b36812858%2F9aqmljg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Transformation Question
#### Problem Statement
What would the image of the vector \( (1, 2, 3) \) be under the transformation modeled by the following matrix?
\[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 2 & 3 & 1
\end{bmatrix}
\]
#### Options
- O (1, 2, 3)
- O (1, 4, 9)
- O (2, 4, 6)
- O (0, 0, 0)
This exercise involves applying a matrix transformation to a 3D vector in homogeneous coordinates. The matrix given is a 4x4 transformation matrix, often used in 3D graphics and computational geometry. The problem is designed to test understanding of matrix-vector multiplication and transformation applications.
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