30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01 whose co-ordinates are represented by the matrix A = Lo o 11 6 6
30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01 whose co-ordinates are represented by the matrix A = Lo o 11 6 6
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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![**Reflection and Matrices**
**Problem Statement:**
You are given that reflection about the origin is represented by the matrix:
\[ R_0 = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \]
You need to apply this reflection to the letter whose coordinates are represented by the matrix:
\[ A = \begin{bmatrix} 0 & 4 & 4 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 6 & 6 \end{bmatrix} \]
**Explanation:**
1. **Matrix \(R_0\)**: This is a transformation matrix that reflects points about the origin. The matrix \(\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}\) means that both the x-coordinates and y-coordinates of any point will be inverted (multiplied by -1).
2. **Matrix \(A\)**: This matrix contains coordinates of a shape (here referred to as "the letter") in a 2D space.
- The first row represents the x-coordinates: \([0, 4, 4, 1, 1, 0]\).
- The second row represents the y-coordinates: \([0, 0, 1, 1, 6, 6]\).
**Goal**: Multiply matrix \(R_0\) with matrix \(A\) to find the new coordinates of the letter after reflection about the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0698be9-21e6-4e48-877e-e3169fefd89c%2F0a5e0aeb-3ffd-4031-89f3-0c08081c18fc%2Fvjbfu3d_processed.png&w=3840&q=75)
Transcribed Image Text:**Reflection and Matrices**
**Problem Statement:**
You are given that reflection about the origin is represented by the matrix:
\[ R_0 = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \]
You need to apply this reflection to the letter whose coordinates are represented by the matrix:
\[ A = \begin{bmatrix} 0 & 4 & 4 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 6 & 6 \end{bmatrix} \]
**Explanation:**
1. **Matrix \(R_0\)**: This is a transformation matrix that reflects points about the origin. The matrix \(\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}\) means that both the x-coordinates and y-coordinates of any point will be inverted (multiplied by -1).
2. **Matrix \(A\)**: This matrix contains coordinates of a shape (here referred to as "the letter") in a 2D space.
- The first row represents the x-coordinates: \([0, 4, 4, 1, 1, 0]\).
- The second row represents the y-coordinates: \([0, 0, 1, 1, 6, 6]\).
**Goal**: Multiply matrix \(R_0\) with matrix \(A\) to find the new coordinates of the letter after reflection about the origin.
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