1. Multiply the following matrices; if you can't multiply the matrices, then explain why. 2 -3 1 1 3 - A. 0 4 2 2 1 1 0 -3) 0 5 3 1 5 1 B. -2 0 2-3 1 0 4 2 1 0 - 3
1. Multiply the following matrices; if you can't multiply the matrices, then explain why. 2 -3 1 1 3 - A. 0 4 2 2 1 1 0 -3) 0 5 3 1 5 1 B. -2 0 2-3 1 0 4 2 1 0 - 3
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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![### Matrix Multiplication Exercise
**Problem 1:**
Multiply the following matrices; if you can't multiply the matrices, then explain why.
#### A.
\[
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end{array} \right)
\]
#### B.
\[
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\]
### Instructions:
1. **Matrix Multiplication Rule**: To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.
2. **Procedure**: For valid matrices, calculate the product by taking the dot product of rows from the first matrix with columns from the second matrix.
### Solution Outline:
- **Matrix A** has dimensions \(3 \times 3\).
- **Matrix B** (first matrix in the second problem) has dimensions \(3 \times 2\) for the first matrix and \(3 \times 3\) for the second one.
- **Matrix Product**:
- Matrix A (3x3) and Matrix B (3x2) can be multiplied.
- In the case of problem B, since the first matrix has dimensions of 3x2 and the second matrix is 3x3, the multiplication is not possible according to the multiplication rule.
### Calculation:
For **Problem A**:
\[
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1799000-33ab-4b28-9bb2-f03cfa8defbf%2F5fe29974-88c9-4672-a5f4-3193023037cb%2Ftaiwwxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Multiplication Exercise
**Problem 1:**
Multiply the following matrices; if you can't multiply the matrices, then explain why.
#### A.
\[
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end{array} \right)
\]
#### B.
\[
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\]
### Instructions:
1. **Matrix Multiplication Rule**: To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.
2. **Procedure**: For valid matrices, calculate the product by taking the dot product of rows from the first matrix with columns from the second matrix.
### Solution Outline:
- **Matrix A** has dimensions \(3 \times 3\).
- **Matrix B** (first matrix in the second problem) has dimensions \(3 \times 2\) for the first matrix and \(3 \times 3\) for the second one.
- **Matrix Product**:
- Matrix A (3x3) and Matrix B (3x2) can be multiplied.
- In the case of problem B, since the first matrix has dimensions of 3x2 and the second matrix is 3x3, the multiplication is not possible according to the multiplication rule.
### Calculation:
For **Problem A**:
\[
\left( \begin{array}{ccc}
2 & -3 & 1 \\
0 & 4 & 2 \\
1 & 0 & -3
\end{array} \right)
\cdot
\left( \begin{array}{ccc}
1 & 3 \\
-2 & 1 \\
0 & 5
\end
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