Find the value of a32 if matrix A is the transpose of matrix J. 1 A = Jt and J %3D 4 5
Find the value of a32 if matrix A is the transpose of matrix J. 1 A = Jt and J %3D 4 5
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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![### Question 24
**Problem:**
Find the value of \( a_{32} \) if matrix \( A \) is the transpose of matrix \( J \).
Given:
\[ A = J^t \]
\[ J = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]
**Explanation:**
1. **Matrix Transposition:**
- The transpose of a matrix \( J \), denoted as \( J^t \), is obtained by swapping its rows and columns.
2. **Transpose of Matrix \( J \):**
- Original matrix \( J \) is a \( 2 \times 3 \) matrix:
\[
J = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
\]
- Transpose will be a \( 3 \times 2 \) matrix \( A \):
\[
J^t = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}
\]
3. **Finding \( a_{32} \):**
- Matrix \( A = J^t \) is:
\[
A = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}
\]
- The element \( a_{32} \) refers to the element in the 3rd row, 2nd column of matrix \( A \).
- Thus, \( a_{32} = 6 \).
**Conclusion:**
The value of \( a_{32} \) is 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F855418f3-d840-444d-b866-5c675da27c94%2F53b38f37-5b50-49f0-a03a-bd90b59f2b00%2F1av01no_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 24
**Problem:**
Find the value of \( a_{32} \) if matrix \( A \) is the transpose of matrix \( J \).
Given:
\[ A = J^t \]
\[ J = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]
**Explanation:**
1. **Matrix Transposition:**
- The transpose of a matrix \( J \), denoted as \( J^t \), is obtained by swapping its rows and columns.
2. **Transpose of Matrix \( J \):**
- Original matrix \( J \) is a \( 2 \times 3 \) matrix:
\[
J = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
\]
- Transpose will be a \( 3 \times 2 \) matrix \( A \):
\[
J^t = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}
\]
3. **Finding \( a_{32} \):**
- Matrix \( A = J^t \) is:
\[
A = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}
\]
- The element \( a_{32} \) refers to the element in the 3rd row, 2nd column of matrix \( A \).
- Thus, \( a_{32} = 6 \).
**Conclusion:**
The value of \( a_{32} \) is 6.
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