# Given the technology matrix, A, and the production vector, X, below: A = [ .5 0 .2 ] X = [ 264 ] [ .2 .8 .12 ] [ 715 ] ...

Given the technology matrix, A, and the production vector, X, below:

A = [ .5 0 .2 ] X = [ 264 ]

[ .2 .8 .12 ] [ 715 ]

[ 1 .4 0 ] [ 585 ]

Compute the demand vector, D.

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### 1 Answer

We use `X=AX+D` which implies `D=X-AX`

We are given `A=([.5,0,.2],[.2,.8,.12],[1,.4,0])` and `X=([264],[715],[585])`

So `D=([264],[715],[585])-([.5,0,.2],[.2,.8,.12],[1,.4,0])([264],[715],[585])`

`=([264],[715],[585])-([249],[695],[550])`

`=([15],[20],[35])`

The external demand matrix is `D=([15],[20],[35])`