Use 3-digit arithmetic with no pivoting?

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Homework Help Overview

The problem involves solving a system of linear equations using 3-digit arithmetic without pivoting. The equations presented are 10 - 3x - y = 1 and x + y = 0.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the Gauss-Jordan method and the setup of the augmented matrix. There are attempts to clarify the arithmetic involved in the calculations, particularly regarding the implications of using 3-digit precision.

Discussion Status

Some participants have provided guidance on setting up the problem and suggested alternative methods to solve the equations. There is a mix of approaches being explored, and one participant has indicated they have resolved the issue independently.

Contextual Notes

Participants are working under the constraint of using 3-digit arithmetic, which may affect the accuracy of their calculations. The original poster's mention of the arithmetic result 10 - 3 = 0.001 raises questions about the precision and assumptions in their calculations.

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Homework Statement


Use 3-digit arithmetic with no pivoting to solve the following system:

10-3x-y=1,
x+y=0.


Homework Equations


I know that 10-3=0.001.


The Attempt at a Solution


The answer for this problem is (0, -1).
Here's the work:
1.001 0
1 1

I've set the augmented matrix and tried using the Gauss-Jordan method to solve the system but I got x=1/1.001 and y=-1/1.001, of course that's not the answer. How do I do this problem?
 
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Using Gauss-Jordian method, the matrix you should start off with is

\begin{pmatrix} 10^{-3} & -1 & 1 \\ 1 & 1 & 0 \end{pmatrix}
 
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Thank you. Don't answer this question anymore. I've already solved it. Thanks again, everyone.
 
I wouldn't bother with matrices. Subtracting .001x+ y= 0 from x+ y= 1, y is eliminated, and we have .999x= 1. Divide both sides by .999, stopping at three decimal places.
 

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