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4. An n x n lower triangular matrix is one whose entries above the main diagonal are all 0. When is a lower triangular matrix invertible? Give an explanation.

4. An n x n lower triangular matrix is one whose entries above the main diagonal are all 0. When is a lower triangular matrix invertible? Give an explanation.

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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**Matrix Invertibility Problems** 3. Can a square matrix with two identical rows be invertible? Why or why not? 4. An \( n \times n \) lower triangular matrix is one whose entries above the main diagonal are all 0. When is a lower triangular matrix invertible? Give an explanation. 5. Let \( A \) and \( B \) be \( n \times n \) matrices. Show that if \( AB \) is invertible, then \( A \) and \( B \) are invertible.
Transcribed Image Text:**Matrix Invertibility Problems** 3. Can a square matrix with two identical rows be invertible? Why or why not? 4. An \( n \times n \) lower triangular matrix is one whose entries above the main diagonal are all 0. When is a lower triangular matrix invertible? Give an explanation. 5. Let \( A \) and \( B \) be \( n \times n \) matrices. Show that if \( AB \) is invertible, then \( A \) and \( B \) are invertible.
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4.  An n×n lower triangular matrix is one whose entries above the main diagonal are all 0.  We have to show when is a lower triangular matrix invertible.

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