A and B are nxn matrices. Check the true statements below: A. det A¹-(-1) det A. OB. If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the origina OC. I det A is zero, then two rows or two columns are the same, or a row or a column is zero. D. The determinant of A is the product of the diagonal entries in A
A and B are nxn matrices. Check the true statements below: A. det A¹-(-1) det A. OB. If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the origina OC. I det A is zero, then two rows or two columns are the same, or a row or a column is zero. D. The determinant of A is the product of the diagonal entries in A
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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Topic: Determinants
Transcribed Image Text:**Matrices and Determinants**
*A and B are n x n matrices.*
**Check the true statements below:**
- □ **A.** \(\text{det} \, A^T = (-1) \, \text{det} \, A\).
- □ **B.** If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix.
- □ **C.** If \(\text{det} \, A\) is zero, then two rows or two columns are the same, or a row or a column is zero.
- □ **D.** The determinant of A is the product of the diagonal entries in A.
**Explanation:**
These options explore properties of determinants in matrices. Each statement can be analyzed to determine its truth based on the known properties of matrix operations and determinants.
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