How to solve Gauss Jordan Elimination with two rows of leading entries of 0?

Question

This is the question:
[ 2 -4 -1 | 0 ]
[ 4 -8 3 | 0 ]
[-3 6 5 | 0 ]

Please help me solve the above problem with gauss-jordan elimination. I'm facing problem half way through when i obtain the bottom two rows both having a leading entry of 0 as following :

[ 1 -2 -1/2 ]
[ 0 0 5 ]
[ 0 0 7/2 ]

did i do anything wrong above? Can someone please help me solve the above question and it will be much appreciated! THank you in advance!! :)

Answer 1

Lordy, Lordy, I wish I knew.............

Answer 2

above explanation is correct , THis has no exact solution
it could have the most general solution of (2t, -t , 0) t is any real value. just by looking at it you realize that.

in normal G J elimination when this sort of thing (zero on a diagonal element) happens you can interchange two rows and carry on doing gauss jordan process again. But for this one ther is no exact solution

Answer 3

Though it looks like it at first, you do not have 3 independent equations. If your constants are a, b, and c, c=0, and the identity of the equations becomes obvious. It works out 2a = 4b, and that's the best you can do.

Answer 4

You did everythign right, but you're out of luck. Your matrix is not linearly independent, so there is no exact numerical solution. Sorry. It can't be solved using a standard Gaussian elimination algorithm.

Answer 5

x + y = 5 + 2z 2x + 3y = 2 - 4z multiply the first equation by -2 and add it to the second -2x - 2y = -10 - 4z 2x + 3y = 2 - 4z ----------------------- ..........y = - 8 - 8z plug this in the first equation x + ( - 8 - 8z) = 5 + 2z x = 13 + 10 z solution is x = 13 + 10 t y = - 8 - 8t z = t