51. Incorrect. The answer is true not false. Recall that in the input output matrix, the inputs into X1 go down, inputs in X2 go down, etc. So the input output matrix is

A	X1	X2	X3	X4
X1	0.10	0.12	0.15	0.16
X2	0.11	0.30	0.17	0.18
X3	0.20	0.25	0.13	0.14
X4	0.40	0.21	0.40	0.22

For the equations, we need X1 inputs into each of the outputs, which go across. So the equations are:

X1 = 0.10X1 + 0.12X2 + 0.15X3 + 0.16X4 + 12

X2 = 0.11X1 + 0.30X2 + 0.17X3 + 0.18X4 + 15

X3 = 0.20X1 + 0.25X2 + 0.13X3 + 0.14X4 + 150

X4 = 0.40X1 + 0.21X2 + 0.40X3 + 0.22X4 + 10

The first four expressions to the right of the equal sign are the amount of X1 used as intermediate product and the last expression 12 is the end- use demand. The solution to this problem is:

X1=144.223

X2=196.141

X3=309.973

X4=298.549