https://file.aiquickdraw.com/mathbot/file/172676371877281oqrx6d.jpg

Let's go over the question visible in your image.

The question is asking for the **composite transformation** \( A \) followed by \( B \), where:

- Matrix \( A = \begin{pmatrix} 2 & 0 \\ -1 & 3 \end{pmatrix} \)
- Matrix \( B = \begin{pmatrix} 1 & 2 \\ -2 & -3 \end{pmatrix} \)

To find the composite transformation, we need to calculate the product \( B \times A \) (Matrix \( A \) followed by \( B \)).

Let me compute that for you.

We are multiplying:

\[
B \times A = \begin{pmatrix} 1 & 2 \\ -2 & -3 \end{pmatrix} \times \begin{pmatrix} 2 & 0 \\ -1 & 3 \end{pmatrix}
\]

Now, I will compute the result.The composite transformation \( B \times A \) is:

\[
\begin{pmatrix} 0 & 6 \\ -1 & -9 \end{pmatrix}
\]

Now, looking at the available answer options in the image, the correct option matches the matrix:

\[
\begin{pmatrix} 0 & 6 \\ -1 & -9 \end{pmatrix}
\]

Let me know if you'd like any further clarification or details!

---

Here are some related questions to deepen your understanding:

1. What is the process for multiplying two 2x2 matrices?
2. How does matrix multiplication apply to transformations in geometry?
3. Can you find the inverse of matrix \( A \)? How is it useful?
4. How does the order of matrix multiplication affect the result?
5. What are some real-life applications of matrix transformations?

**Tip:** When performing matrix multiplication, always ensure the number of columns in the first matrix matches the number of rows in the second matrix.

In the next question, the transformation A is represented by the matrix A = (2 0 \n -1 3) and the transformation B is represented by the matrix B = (1 2 \n -2 -3). The composite transformation A followed by B is represented by the matrix?

Discover how to compute the composite transformation of two matrices. In this problem, we are tasked with finding the product of matrices A and B, representing sequential transformations. This is an essential concept in linear algebra and transformations. Suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation