Input output model

[Neel Tulsan]

Hi. I've managed to solve the cramer's rule for the input output model below.
Assuming X =AX + D
or X = inverse(I-A).D

The input output model for the following sectors have been input below.
		in Millions$
	Agriculture	Manufacture	Energy
Agriculture	11	3	0
Manufacture	1	13	4
Energy	0	1	10
Total	12	17	14
Find the technology matrix A
Assuming a rise in external demand for agriculture of $3million and Manufacture $2million, find:
(ii) the system of linear equation that would give the change in production?
(iii) the change in production using Cramer's Rule

My solution is attached. Am I doing it well?

Thanks