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Let A be an nxn matrix. Which of the following statements is/are NOT equivalent to that A is invertible? (1) The columns of AT form a basis for R. ii) The nullity of AT is 0. lii) The non-homogeneous system ATX = b has a unique solution for any choice of bin R. iv) O is not an eigenvalue for AT. Selected Answer: Answers: iv) only ii), ii), and iv) only I) and iv) only iii) and iv) only li) and iii) only iv) only

Let A be an nxn matrix. Which of the following statements is/are NOT equivalent to that A is invertible? (1) The columns of AT form a basis for R. ii) The nullity of AT is 0. lii) The non-homogeneous system ATX = b has a unique solution for any choice of bin R. iv) O is not an eigenvalue for AT. Selected Answer: Answers: iv) only ii), ii), and iv) only I) and iv) only iii) and iv) only li) and iii) only iv) only

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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Question 14 Let A be an nxn matrix. Which of the following statements is/are NOT equivalent to that A is invertible? ) The columns of A' form a basis for R". i) The nullity of A' is 0. lii) The non-homogeneous system A'X b has a unique solution for any choice of b in R". )0 is not an eigenvalue for A'. Selected Answer: iv) only Answers: I), lii), and iv) only 1) and iv) only iil) and iv) only 1) and il) only iv) only
Transcribed Image Text:Question 14 Let A be an nxn matrix. Which of the following statements is/are NOT equivalent to that A is invertible? ) The columns of A' form a basis for R". i) The nullity of A' is 0. lii) The non-homogeneous system A'X b has a unique solution for any choice of b in R". )0 is not an eigenvalue for A'. Selected Answer: iv) only Answers: I), lii), and iv) only 1) and iv) only iil) and iv) only 1) and il) only iv) only
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