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Homework Statement
Balance the following Chemical Equation
(x1)KMnO4+(x2)MnSO4+(x3)H2O->(x4)MnO2+(x5)K2SO4+(x6)H2SO4
Homework Equations
Here is the matrix I came up with but it seems to be flawed but I am unable to see what i am doing wrong
1 0 0 0 -2 0 (K)
0 1 0 -1 0 0 (Mn)
4 4 1 -2 -4 -4 (O)
0 1 0 0 -1 -1 (S)
0 0 2 0 0 -2 (H)
Each column corresponds to the amount of each element in each compound.
This is the reduced row echelon form of the matrix
1 0 0 0 0 -1/3
0 1 0 0 0-7/6
0 0 1 0 0 -1
0 0 0 1 0-7/6
0 0 0 0 1 -1/6
I seem to be missing the free variable I need to solve this problem
The Attempt at a Solution
The answer i come up with is
X1=(1/3)
X2=(7/6)
X3=(1)
X4=(7/6)
X5=(1)
and here is the problem for I only get five answers and not the six that i need to balance the equation. Can anyone point me in a direction or say what I am doing wrong any help will be appreciated thank you.