Use the Gauss–Jordan method to solve the following system of linear equations:
(A system with more variable than equations is calledunderdetermined.)
x+ y − z + 2w = −20
2x − y + z + w = 11
3x − 2y + z − 2w = 27
So putting this into matrices, I get
[1 1 -1 2 | -20]
[2 -1 1 1 | 11 ]
[3 -2 1 -2 | 27]
^ note, that's all supposed to be in one matrix
I've tried over and over again, but I just can't get this system into row-reduced form...can someone please help?
Hello, tuheetuhee!
Use the Gauss–Jordan method to solve the following system of linear equations:
. .
We have: .
. .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We have: .
On the right side, replace with the parameter .
Therefore: .
This represents all the possible solutions of the system.
we put the matrix into reduced row-echelon form here, but no, you do not have to do that when solving any system of equations. it is enough to bring it to row echelon form (the form where all non-zero rows have leading 1's). the difference is, the algebra at the end that you need to do to find the solutions might be a bit more tedious. unless you are told specifically what to do, it is up to you whether you want to work out the algebra or just bring it to reduced row echelon form and do easier algebra.