1 votes 1 votes My solution:- Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ? According to me Option D as rank is < Order so infinite number of solutions Linear Algebra linear-algebra engineering-mathematics system-of-equations + – Na462 asked Oct 25, 2018 Na462 968 views answer comment Share Follow See all 9 Comments See all 9 9 Comments reply Magma commented Oct 25, 2018 reply Follow Share It's D yeah you're correct 0 votes 0 votes Magma commented Oct 25, 2018 reply Follow Share Na462 what's the answer given ?? 0 votes 0 votes Shubhanshu commented Oct 25, 2018 reply Follow Share Option D is correct. 0 votes 0 votes Na462 commented Oct 25, 2018 reply Follow Share Answer given is B, maybe it's wrong. What is condition for no solution In homogenous equations ? 0 votes 0 votes Magma commented Oct 25, 2018 reply Follow Share if in question they mentioned that Number of linearly independent solution then it's equal to 1 1 votes 1 votes Magma commented Oct 25, 2018 reply Follow Share no solution In homogenous equations In homogeneous linear equation always there's a unique solution which is x = y = z = 0 when rank (A) = Number of variable No solution is the case of Non homogenous equations 0 votes 0 votes Na462 commented Oct 25, 2018 reply Follow Share Oh yeah I'm stupid socha nhi mene axche se thnks. Magma Please enlighten this point " if in question they mentioned that Number of linearly independent solution then it's 1 " 0 votes 0 votes Magma commented Oct 25, 2018 reply Follow Share if No of variables = 3 and rank of matrix (A) = 2 No of linear independent solution : 3-2 = 1 which means if a equation is like that x + 3y + 2z = 0 -7y + 8z = 0 therefore Y = (8/7) Z , X = (10/7) Z let Z = c Y = (8/7)c , X = (10/7)C for any arbitrary value of C we can get X and Y therefore no of independent solution = 1 from which we can derive infinite solution Similarly if if No of variables = 3 and rank of matrix (A) = 1 No of linear independent solution : 3-2 = 1 1 votes 1 votes DAWID15 commented Dec 4, 2021 reply Follow Share For a homogeneous equation there are only two possibilities 1. equation has infinite solution if |A| = 0 then equation has infinite solution.(Which is why the option is D for above question) 2. Equation has one solution(trivial) If |A| $\neq$ 0 then the homogeneous equation will always have one solution i.e when the variables x,y,z themselves are equal to 0. Here’s something you can refer : http://www.math.hawaii.edu/~lee/linear/sys-eq.pdf 0 votes 0 votes Please log in or register to add a comment.