0 votes 0 votes True /false If any row/column is constant is constant multiple of any other row/column then determinant is zero. Whether the converse of this statement is true or false? Theory of Computation linear-algebra engineering-mathematics + – rahul sharma 5 asked Jun 29, 2017 rahul sharma 5 395 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Rupendra Choudhary commented Jun 29, 2017 reply Follow Share It's an 'iff' case. Determinant of a Matrix is 0 iff It is linearly dependent. 0 votes 0 votes Smriti012 commented Jun 30, 2017 i edited by Smriti012 Jun 30, 2017 reply Follow Share Converse is not true. 0 votes 0 votes Rupendra Choudhary commented Jun 30, 2017 reply Follow Share Hello smiriti Dependent rows or column means we can get other by simple mltiplication or division here 1*0=0 9*0=0 1*0=0 so from row 2 you can get row 1. you know from where your first row 0 0 0 came? it came by some small calculations which is allowed in determinant . like originally it was 4 14 16 1 9 1 2 7 8 now here row 1 and 3 are dependent and from here you can get the matrix you provided. this is an iff case easily through some vector calculation we can prove it. (you can help web) hope you got my point. 0 votes 0 votes Smriti012 commented Jun 30, 2017 reply Follow Share thankyou,I got my mistake :) 0 votes 0 votes Please log in or register to add a comment.