1 1 vote If the determinant and sum of eigen values of a 2 x 2 matrix are -1 and 0 then, what can you say about the rank of the given matrix? a) rank is 0 b) rank is 1 c) Insufficient information d) rank is 2 Linear Algebra iit-madras written-test admissions linear-algebra + – harshrajhrj 1.0k views answer comment Share Follow Print See all 2 Comments 2 2 Comments reply Shankalp Gaur commented May 2, 2024 reply Follow flag I think ans is c 0 0 replyShare harshrajhrj commented May 2, 2024 reply Follow flag How can you come up with that? 0 0 replyShare Please log in or register to add a comment.
Best answer 7 7 votes Since determinant is non-zero so the Matrix will be invertible and that's why it will have full rank. So $D$ will be ans . ꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered Apr 30, 2024 • selected Apr 30, 2024 by harshrajhrj ꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ comment Share Follow 0 reply Please log in or register to add a comment.
0 0 votes Trace = 0 , one eigen value is -1 , since this is a 2×2 matrix another eigen value is 1. Rank of matrix is 2 since it has 2 distinct eigen values 1 , -1 Bhargobi answered Dec 9, 2024 Bhargobi comment Share Follow 0 reply Please log in or register to add a comment.
