Solve the problem.
-The input-output matrix for an economy is Find the production matrix X.

Question

Solve the problem.
-The input-output matrix for an economy is  Find the production matrix X.

Quizplus · Accepted Answer

To find the production matrix X, we need to perform row operations to bring the input-output matrix into the identity matrix. 
11ebb17b_2a00_eea7_afdc_f706dfd171f7_TB8591_00 → 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1

The row operations required are not provided in the answer choices, so we must manually perform the row operations:

Row 2 + Row 1 → Row 2 
11ebb17b_2a00_eea7_afdc_f706dfd171f7_TB8591_00 → 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1

Row 3 - Row 2 → Row 3 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 e 8 8 8 e 0 3 9 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1

Row 4 - Row 2 → Row 4 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 e 8 8 8 e 0 3 9 
0 0 0 1 e 1 b 1 7 b 
0 0 0 0 1 0 
0 0 0 0 0 1

Row 5 - Row 2 → Row 5 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 e 8 8 8 e 0 3 9 
0 0 0 1 e 1 b 1 7 b 
0 0 0 0 1 e 7 1 
0 0 0 0 0 1

Row 6 - Row 2 → Row 6 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 e 8 8 8 e 0 3 9 
0 0 0 1 e 1 b 1 7 b 
0 0 0 0 1 e 7 1 
0 0 0 0 0 e 9 9

Row 3 ÷ e → Row 3 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 0 1 1 1 3 
0 0 0 1 e 1 b 1 7 b 
0 0 0 0 1 e 7 1 
0 0 0 0 0 e 9 9

Row 4 - Row 5e → Row 4 
1 0 0 0 0 0 
1 e 1 b 1 b 1 7 b 
0 0 1 1 1 3 
0 0 0 0 1 9 e 
0 0 0 0 1 e 7 1 
0 0 0 0 0 e 9 9

The last three rows have non-zero elements that cannot be simplified to zero, indicating that there is not a unique solution. This is characteristic of an underdetermined system, and we must choose the option that best approximates the solution. The answer is C, as it is closest to the achieved row echelon form.

Solve the Problem. -The Input-Output Matrix for an Economy Is Find the