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8.42. True or False. Let A, B, C be three 4 x 4 matrices. If ABC is not singular, then one of the three matrices must have linearly dependent rows. 8.43. True or False. If det (A) = 1, then A must be the identity matrix.

8.42. True or False. Let A, B, C be three 4 x 4 matrices. If ABC is not singular, then one of the three matrices must have linearly dependent rows. 8.43. True or False. If det (A) = 1, then A must be the identity matrix.

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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### Linear Algebra Multiple-Choice Questions #### 8.42 True or False: Let \( A \), \( B \), \( C \) be three \( 4 \times 4 \) matrices. If \( ABC \) is not singular, then one of the three matrices must have linearly dependent rows. #### 8.43 True or False: If \( \text{det}(A) = 1 \), then \( A \) must be the identity matrix. Understanding whether a composite matrix is singular or assessing the determinant of a matrix provides essential insights into matrix properties and their implications in linear algebra. For detailed solutions and further explanations, please refer to the study material provided in this section.
Transcribed Image Text:### Linear Algebra Multiple-Choice Questions #### 8.42 True or False: Let \( A \), \( B \), \( C \) be three \( 4 \times 4 \) matrices. If \( ABC \) is not singular, then one of the three matrices must have linearly dependent rows. #### 8.43 True or False: If \( \text{det}(A) = 1 \), then \( A \) must be the identity matrix. Understanding whether a composite matrix is singular or assessing the determinant of a matrix provides essential insights into matrix properties and their implications in linear algebra. For detailed solutions and further explanations, please refer to the study material provided in this section.
8.42 False. 8.43 False.
Transcribed Image Text:8.42 False. 8.43 False.
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