2. Given the matrices A and B, find the products AB and BA 132 23 A = -2 14 B = 14
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 Multiplication Problem
**Task:**
Given the matrices \( A \) and \( B \), find the products \( AB \) and \( BA \).
**Matrices:**
Matrix \( A \):
\[
A = \begin{bmatrix} 1 & 3 & 2 \\ -2 & 1 & 4 \end{bmatrix}
\]
Matrix \( B \):
\[
B = \begin{bmatrix} 2 & 3 \end{bmatrix}
\]
### Explanation:
- **Matrix \( A \)** is a 2x3 matrix with two rows and three columns.
- **Matrix \( B \)** is a 1x2 matrix with one row and two columns.
To find the products:
- \( AB \) requires that the number of columns in \( A \) matches the number of rows in \( B \). Here, they do not match, so \( AB \) cannot be computed in the standard way.
- Similarly, \( BA \) requires that the number of columns in \( B \) matches the number of rows in \( A \). Here, the dimensions do not allow \( BA \) to be computed either.
### Conclusion:
The multiplication \( AB \) and \( BA \) is not defined for the given matrices due to dimension incompatibility. Matrix multiplication can only be performed when the number of columns in the first matrix equals the number of rows in the second matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4971acb-5e4c-4bbe-8a68-29fa1157d0f8%2F33fd861e-f7d0-4ee1-88c2-2873c075e3bc%2Fnczx44c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Multiplication Problem
**Task:**
Given the matrices \( A \) and \( B \), find the products \( AB \) and \( BA \).
**Matrices:**
Matrix \( A \):
\[
A = \begin{bmatrix} 1 & 3 & 2 \\ -2 & 1 & 4 \end{bmatrix}
\]
Matrix \( B \):
\[
B = \begin{bmatrix} 2 & 3 \end{bmatrix}
\]
### Explanation:
- **Matrix \( A \)** is a 2x3 matrix with two rows and three columns.
- **Matrix \( B \)** is a 1x2 matrix with one row and two columns.
To find the products:
- \( AB \) requires that the number of columns in \( A \) matches the number of rows in \( B \). Here, they do not match, so \( AB \) cannot be computed in the standard way.
- Similarly, \( BA \) requires that the number of columns in \( B \) matches the number of rows in \( A \). Here, the dimensions do not allow \( BA \) to be computed either.
### Conclusion:
The multiplication \( AB \) and \( BA \) is not defined for the given matrices due to dimension incompatibility. Matrix multiplication can only be performed when the number of columns in the first matrix equals the number of rows in the second matrix.
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