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Algebra/system of linear Equation and Matrices


(1) Please help me solve this equation by Using Gauss-Jordan method



(2) Find the production matrix for the following input-output and demand matrics using open model

A= [ o.1]   [0.03]       D= [5][10]  
  [0.07]   [0.6 ]

My computer got hung up for awhile and I wasn't able to answer questions,
but I think that it has been freed from this problem ... at least so far, so good.

The Gauss-Jordan method makes that matrix have ones in the diagonal with 0's down below.
For the matrix
4 -2  3
-2  3  1,
the first step would be to divide the 1st row by 4 and
at the same time add half of the first row to the second row.

This would give us the matrix
1  -0.5  0.75
0   2.0  3.00  { with the numbers written with same number of digits to align them better }.

The next things to do would be to divide the 2nd row by 2, giving
1  -0.5  0.75
0   1.0  1.50.

Once in this form, the solution is x2 = 1.5.
Using x1 - 0.5x2 = 0.75, this says x1 -.75 = 0.75, so x1 = 1.5 as well.

For large matrices, this allows the matrix to be solved with far fewer steps than zeroing out the entire column.


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Scott A Wilson


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