   Solving linear equations
  This was a test run for my SquareMatrix class. The augmented matrix to be solvedis this :1 2 3| 14 5 6| 17 8 9| 1The answer it spat out was {-0.659 ,0.318,0.341 }By trying this into the matrix, it seems that its correct. So{1,2,3} dot{-0.659 0.318 0.341} = 1{4,5,6} dot{-0.659 0.318 0.341} = 1{7,8,9} dot{-0.659 0.318 0.341} = 1But I'm using this online calculator and the answer it spat out was :{-2.500, 4.000, -1.500}I don't see why this matrix has 2 solutions? I mean there are all basic variables and no free variables, so it should only have 1 solution set. Yet bothof those solution works? How comes?------------------Edit :The thing is that for this augmented matrix :1 2 | 13 4 | 1the answer my class spat out is {-1,1} and the answer the online calculatorspat out is {-1,1}; which is the same. So I'm not sure.   
  The problem is that your matrix has rank 2. You can see that the second row is the average of the first and the third rows. In other words, you don't really have 3 equations, but only 2.To check if your matrix is degenerate, compute its determinant. If it's 0, that's trouble.   ;  The solution your matrix class gave you was only one of many, since as alvaro pointed out your matrix isn't full rank.  In this particular case your solution space is a line, as opposed to a single point (you have one free variable).  The different specific solutions can be attributed to different processes being used by your matrix class and the online calculator.  However the null space still needs to be determined if you want to find the complete solution.EDIT: Actually, you can determine the null space from those two solutions.  Exercise left to reader [grin]   ;  >> The problem is that your matrix has rank 2Oh dang. I probably did some calculation by hand, wrong then. Thanks. I wasunder the impression that, It had rank 3. Thanks for the info. Oh andits determinant is 0. Thanks.>> Actually, you can determine the null space from those two solutions. Exercise left to reader Oh no. Got so tired of doing those problems, in my class. Thanks for the offer though.