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] Determinant of a triangular matrix. Consider the following matrix a11 a12 a13 0 a22 a23 a33 0 0 A = This matrix is said to be in upper-triangular form. Show that the determinant of this matrix is given by the product of the diagonal elements, i.e. |A| = a11 a22 a33

] Determinant of a triangular matrix. Consider the following matrix a11 a12 a13 0 a22 a23 a33 0 0 A = This matrix is said to be in upper-triangular form. Show that the determinant of this matrix is given by the product of the diagonal elements, i.e. |A| = a11 a22 a33

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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Show full answers and steps to this exercise - Use property I: The interchange of rows & columns doesn’t change the value of the determinant
[15] Determinant of a triangular matrix. Consider the following matrix a11 A = 0 0 a12 a22 0 a 13 a23 a33 This matrix is said to be in upper-triangular form. Show that the determinant of this matrix is given by the product of the diagonal elements, i.e. |A| = a11 a22 a33
Transcribed Image Text:[15] Determinant of a triangular matrix. Consider the following matrix a11 A = 0 0 a12 a22 0 a 13 a23 a33 This matrix is said to be in upper-triangular form. Show that the determinant of this matrix is given by the product of the diagonal elements, i.e. |A| = a11 a22 a33
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