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where the superscript - 1 indicates the operation of matrix 
inversion. Now each column of the inverted matrix represents 
the amounts of all intermediate goods which have gone into 
one unit of final commodity. This means that by multiplying 
each column of the inverted matrix by the row of the input- 
output labour coefficients which has been excluded from (VI.1), 
we arrive at the labour coefficients of the vertically integrated 
system. 
[n algebraic terms: 
1 
where the mark ’ denotes the operation of matrix transposition. 
Equations (VI.3) now give the algebraic relation, existing in a 
ziven period of time, between the labour coefficients of an 
input-output model and the labour coefficients of the vertically 
ntegrated sectors used in the present dynamic model. The 
ones may be obtained from the others — as the (VI.3) now 
directly show — by a straight-forward algebraical operation. 
>. Fitting empirical data into the moael 
The algebraic relation which has just been obtained and 
which links the input-output technical coefficients with the tech- 
aical coefficients of our analysis finds an immediate applica: 
ro] Pasinetti - pag. 99