Insumo Producto Ieontief

El valor total de la industria gobierno, agricultura y manufactura es 1000, 1000, 1000,

Respectivamente, luego

A=[■(400/1000&200/1000&200/1000@200/1000&400/1000&100/1000@200/1000&100/1000&300/1000)]=

[■(2/5&1/5&1/5@1/5&2/5&1/10@1/5&1/10&3/10)]

I-A=[■(1&0&0@0&1&0@0&0&1)]-[■(2/5&1/5&1/5@1/5&2/5&1/10@1/5&1/10&3/10)]=

[■(3/5&-1/5&-1/5@-1/5&3/5&-1/10@-1/5&-1/10&7/10)]

Se evalúa 〖(I-A)〗^(-1) utilizando la adjunta

c_11=〖(-1)〗^(1+1) |■(3/5&-1/10@-1/10&7/10)|=(-1)^(1+1) (3/5)(7/10)-(-1/10)(-1/10)=41/100

c_12=〖(-1)〗^(1+2) |■(-1/5&-1/10@-1/5&7/10)|=〖(-1)〗^(1+2) (-1/5)(7/10)+(-1/5)(-1/10)=4/25

c_13=〖(-1)〗^(1+3) |■(-1/5&3/5@-1/5&-1/10)|=(-1)^(1+3) (-1/5)(-1/10)-(-1/5)(3/5)=7/50

En este punto puede evaluarse |I-A| sobre el renglón uno utilizando cofactores.

|I-A|=3/5 (41/100)-1/5 (4/25)-1/5 (7/50)=93/500

Se calculan los demás cofactores c_21=(-1)^(2+1) |■(-1/5&-1/5@-1/10&7/10)|=(-1)^(2+1) (-1/5)(7/10)+(-1/10)(-1/5)=4/25

c_22=(-1)^(2+2) |■(3/5&-1/5@-1/5&7/10)| 〖=(-1)〗^(2+2) (3/5)(7/10)-(-1/5)(-1/5)=19/50

c_23=(-1)^(2+3) |■(3/5&-1/5@-1/5&-1/10)|=(-1)^(2+3) (3/5)(-1/10)+(-1/5)(-1/5)=1/10

c_31=(-1)^(3+1) |■(-1/5&-1/5@3/5&-1/10)|=(-1)^(3+1) (-1/5)(-1/10)-(3/5)(-1/5)=7/50

c_32=(-1)^(3+2) |■(3/5&-1/5@-1/5&-1/10)|=(-1)^(3+2) (3/5)(-1/10)+(-1/5)(-1/5)=1/10

c_33=(-1)^(3+3) |■(3/5&-1/5@-1/5&3/5)|=(-1)^(3+3) (3/5)(3/5)-(-1/5)(-1/5)=8/25

(I-A)^(-1)=1/|I-a| adj(I-A)

=500/93 [■(41/100&4/25&7/50@4/25&19/50&1/10@7/50&1/10&8/25)]=

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