Question

请问这道线性代数题如何求解？

请给出详细解答，多谢

Answer 1

a)
It can be shown that a consumption matrix is productive if and only if there is a vector such that
x>Cx

I-C= .4 -.8
-.1 .6
x= 3
1
(I-C)x= .4
.3
So(I-C)x>0
x>Cx
It is productive

b)
(I-C)p=d
Use row transformation
.4 -.8 700
-.1 .6 600

row1 /.4
row2 *10
1 -2 1750
-1 6 6000
row2=row1+row2
1 -2 1750
0 4 7750
row2/4
1 -2 1750
0 1 1937.5
row1=row1+row2*2
1 0 5625
0 1 1973.5
p= 5625
1973.5