] 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2Fd588fffd-5f63-4fab-8697-e79a8ab667e4%2Fvu3s6zb_processed.jpeg&w=3840&q=75)
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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