Solving matrix by hand - Gaussian-Jordan I am trying to solve the following matrix. I tried to use Gaussian-Jordan elimination, but I can figure it out. Can some one show me how to find i1, i7 and i8. I can solve this matrix with help from a math software, but I want to do it by hand. 
Also I tried to solve the matrix equations by substitution, but this is very laborious.

$$
\left[ \begin {array}{ccc} r_{g}+r_{b}&amp;-r_{b}&amp;0
\\r_{b}&amp;r_{{\it a1}}&amp;r_{{\it a2}}\\
r_{g}&amp;r_{{\it a1}}+
r_{{\it gr}}&amp;-r_{{\it gr}}-r_{j}\end {array} \right]*
\left[ \begin {array}{ccc} i_{1}
\\i_{7}\\
i_{8}\end {array} \right]=\left[ \begin {array}{ccc} 4u
\\4u\\
u\end {array} \right]
$$

The software did not give an echelon form. I give the three equations as input and then used the solve commando. If the Gaussian-Jordan method is not possible, are the only ways to solve this matrix by usage of substitution or Cramer?
$A \cdot X=B$ can be solved (if A is invertible) as $X=A^{-1}\cdot B$

So the fastest way to solve this equation is to find $A^{-1}$and to multiply by B.
Finding an echelon form for a matrix with variable entries can be problematic, because the echelon form depends on whether this or that equals zero. To take a simpler example, one really cannot say what the reduced echelon form for the matrix $$\left[\begin{matrix}a&amp;b\\c&amp;d\end{matrix}\right]$$is; it could be any $2\times2$ reduced-echelon-form matrix. The software that gave you an echelon form for your matrix must be making some unwarranted assumptions.