Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Solve and find the missing values
![The image shows a mathematical equation involving matrix multiplication. It is structured as follows:
\[
\begin{bmatrix} a & b \\ c & d \end{bmatrix} \cdot \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix} = \begin{bmatrix} 10 & 11 \\ 20 & 29 \end{bmatrix}
\]
### Explanation:
- **Left Matrix**: A 2x2 matrix with elements \(a, b, c,\) and \(d\).
- **Middle Matrix**: Another 2x2 matrix with values:
- First row: 4, 3
- Second row: 2, 5
- **Resulting Matrix**: The product of the matrices, also a 2x2 matrix with values:
- First row: 10, 11
- Second row: 20, 29
This equation represents the multiplication of two matrices resulting in a third matrix. The elements of the resulting matrix are derived by calculating the dot products of the rows from the first matrix with the columns of the second matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefea87ef-0421-4819-8f88-3243a5ec5deb%2Fbfb80680-f146-48c1-a120-c21df5cc47f2%2Fxavi68k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical equation involving matrix multiplication. It is structured as follows:
\[
\begin{bmatrix} a & b \\ c & d \end{bmatrix} \cdot \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix} = \begin{bmatrix} 10 & 11 \\ 20 & 29 \end{bmatrix}
\]
### Explanation:
- **Left Matrix**: A 2x2 matrix with elements \(a, b, c,\) and \(d\).
- **Middle Matrix**: Another 2x2 matrix with values:
- First row: 4, 3
- Second row: 2, 5
- **Resulting Matrix**: The product of the matrices, also a 2x2 matrix with values:
- First row: 10, 11
- Second row: 20, 29
This equation represents the multiplication of two matrices resulting in a third matrix. The elements of the resulting matrix are derived by calculating the dot products of the rows from the first matrix with the columns of the second matrix.
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