Chemistry and system of equations

[brad sue]

Hi,
I want to kow if it is possible to convert a chemical equation ( unbalanced)
into a matrix and solve this matrix to find the coeficient of the equations to balance the equations.
For example:
H₂SO₄+MnS+As₂(Cr₂O₇)₅---->HMnO₄+AsH₃+Cr₂(SO₄)₃+H₂O
How to convert it into a matrix of unknowns to find the balanced coefficients?
Thank you
B

 

[quantumdude]

Can you present your thoughts on the matter first?

Thanks.

 

[brad sue]

Can you present your thoughts on the matter first?
Thanks.

I think That I need to produce an system of equation with the coefficient as the coefficient of the molecules ( for each element)
for H : 2, 0, 0, -1, -3, 0, -2
for S : 1, 1, 0, 0, 0, -3, 0
for O :4, 0, 35, -4, 0, -12, -1
for Mn : 0, 1, 0, -1, 0, 0 , 0
for As : 0, 0, 2, 0, -1, 0, 0
for Cr : 0, 0, 10, 0, 0, -2, 0
I don't know if I am right , but when I solve this system , I get some negative coefficients which makes no sense.
Please can you help me to understand what is going on here?
Thank you
B.