Question

Hi everybody, I need to solve the following system of linear equations. I have used the Gauss-Jordan elimination method, but I can't figure out the solution. I have attached my method of solving this problem.

Answer 1

your work is completely correct
so x1-x4=0 --> x1=x4
x2-x3=0 -->x2 =x3
x5=0
the solution is \(\left[\begin{matrix}x1\\x2\\x2\\x1\\x5\end{matrix}\right]\)
Pay attention, you have 3 equations, 5 variables. You will have at least 2 free variables. So that in your solution, you have just 3 dependent variables. That's is correct answer
For example, if you choose x1 =1, x2 =2 then, your solution is \(\left[\begin{matrix}1\\2\\2\\1\\0\end{matrix}\right]\)
And due to the free variables, you have infinite set of solution :
S ={\(\left[\begin{matrix}\alpha\\\beta\\\beta\\\alpha\\0\end{matrix}\right]; \alpha , \beta \in R\) }

Answer 2

Thanks, @Loser66
I understand it now, funny that I didn't see that x1 = x4, and so on.

I appreciate your time :-)!