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Let A = 0 1 2 1 -1 - 3 1 2 2 0 1 0 3-1 1 0 . Find M11, M21, M32, C11, C21, and C32.

Let A = 0 1 2 1 -1 - 3 1 2 2 0 1 0 3-1 1 0 . Find M11, M21, M32, C11, C21, and C32.

Advanced Engineering Mathematics
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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**Exercise 7.2.2** Let \( A = \begin{bmatrix} 0 & -1 & 3 & 1 \\ 1 & 0 & 2 & 2 \\ 2 & 3 & -1 & 0 \\ 1 & 1 & 0 & 1 \end{bmatrix} \). Find \( M_{11}, M_{21}, M_{32}, C_{11}, C_{21}, \) and \( C_{32} \). --- In this exercise, you are given a 4x4 matrix \( A \) and tasked with finding specific minors and cofactors. - **Minor \( M_{ij} \):** Determinant of the submatrix that remains after removing the \( i \)-th row and \( j \)-th column from matrix \( A \). - **Cofactor \( C_{ij} \):** Given by \( C_{ij} = (-1)^{i+j} \cdot M_{ij} \), where \( M_{ij} \) is the minor. Calculate the following: - **\( M_{11} \):** Minor obtained by removing the first row and first column. - **\( M_{21} \):** Minor obtained by removing the second row and first column. - **\( M_{32} \):** Minor obtained by removing the third row and second column. - **\( C_{11}, C_{21}, \) and \( C_{32} \):** Corresponding cofactors for the above minors.
Transcribed Image Text:**Exercise 7.2.2** Let \( A = \begin{bmatrix} 0 & -1 & 3 & 1 \\ 1 & 0 & 2 & 2 \\ 2 & 3 & -1 & 0 \\ 1 & 1 & 0 & 1 \end{bmatrix} \). Find \( M_{11}, M_{21}, M_{32}, C_{11}, C_{21}, \) and \( C_{32} \). --- In this exercise, you are given a 4x4 matrix \( A \) and tasked with finding specific minors and cofactors. - **Minor \( M_{ij} \):** Determinant of the submatrix that remains after removing the \( i \)-th row and \( j \)-th column from matrix \( A \). - **Cofactor \( C_{ij} \):** Given by \( C_{ij} = (-1)^{i+j} \cdot M_{ij} \), where \( M_{ij} \) is the minor. Calculate the following: - **\( M_{11} \):** Minor obtained by removing the first row and first column. - **\( M_{21} \):** Minor obtained by removing the second row and first column. - **\( M_{32} \):** Minor obtained by removing the third row and second column. - **\( C_{11}, C_{21}, \) and \( C_{32} \):** Corresponding cofactors for the above minors.
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