0 votes 0 votes A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is:____________ Linear Algebra linear-algebra + – Hira Thakur asked Nov 28, 2017 Hira Thakur 4.3k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Anu007 commented Nov 28, 2017 reply Follow Share so 4 variables and 3 rows Max rank = min(3,4) = 3 i.e. rank of To make inconsistant rank of [A] = 3-1= 2 i.e. condition for inconsistant => [A|B] not equal to [A] => 3 not equal to 2 So answer is 2 3 votes 3 votes vinay chauhan commented Nov 18, 2018 reply Follow Share Why can't the rank of augmented matrix be 2 and rank of matrix A is 3? 0 votes 0 votes Purva Taranekar commented Dec 1, 2018 reply Follow Share If r([A:B]) is assumed to be 2 then it means that in row echealon form, the last row becomes all 0 for [A:B] , which means the last row for matrix A also becomes all 0, making r(A) = 3-1=2. So only way to make ranks unequal is by making last row of matrix A all 0, but not of [A:B]. 0 votes 0 votes Please log in or register to add a comment.