 Then we might write

or total output equals intermediate output plus final output.If we let formula_9 be the matrix of coefficients formula_4, formula_11 be the vector of total output, and formula_12 be the vector of final demand, then our expression for the economy becomes

which after re-writing becomes formula_14.If the matrix formula_15 is invertible then this is a linear system of equations with a unique solution, and so given some final demand vector the required output can be found.