0 votes 0 votes Linear Algebra matrix rank-of-matrix + – KISHALAY DAS asked Dec 24, 2016 KISHALAY DAS 3.7k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments akashsheoran commented Dec 24, 2016 reply Follow Share Okk...made a mistake... actually if I move 3rd and 4th row up and then exchange first column with 2nd...there is a 3x3 matrix of non-zero determinant. What is the answer...A? 0 votes 0 votes KISHALAY DAS commented Dec 25, 2016 reply Follow Share Ans C 0 votes 0 votes Surajit commented Dec 25, 2016 reply Follow Share When det A = 0 and equations of form AX= 0 and Rank of A < N (order or matrix or no of unknowns) then no of linearly independent solutions are N-rank of matrix. Here its 4-3 =1 no of linearly independent solutions as per my calculation.I dont know how answer C is coming, I feel its wrong.It should be A here. 0 votes 0 votes Please log in or register to add a comment.
Best answer 3 votes 3 votes The rank of the matrix=3 by the method of Row-reduced Echelon form. Now, if there are 'm' linearly independent vectors(or rank of matrix) and 'n' is number of unknows, then #linearly independent solutions = n - m (m<=n) So,here, #linearly independent solutions = 4 - 3 = 1 So, A should be the correct answer. Ref: http://math.stackexchange.com/questions/1235474/the-number-of-linearly-independent-solution-of-the-homogeneous-system-of-linear Sushant Gokhale answered Dec 25, 2016 • selected Dec 25, 2016 by KISHALAY DAS Sushant Gokhale comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Yes, A is right. zeinab answered Nov 25, 2017 zeinab comment Share Follow See all 0 reply Please log in or register to add a comment.