A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns.

Clifland 2020-11-09 Answered
A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns.
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Nathalie Redfern
Answered 2020-11-10 Author has 99 answers

The system of linear equation with unknown lesser than the equations.
Step 2
Concept:
Over-determined system of equations is the system of linear equation with unknowns lesser than the equations.
Step 3
The over-determined system is inconsistent with the irregular coefficients. With linear equations they are consistent.
To consider a system with three equations but two unknowns,
x1+x2=3
2x1x2=0
3x1+3x2=9
The augmented matrix of the above equations is given below
[113210339]
To apply row application
[113210339][113036000]
To simplify row 1 and 2
[113012000][101012000]
The corresponding system of equation is given below,
x1=1
x2=2
The system of equation is consistent and have its unique solution

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Jeffrey Jordon
Answered 2021-10-12 Author has 2064 answers

Step 1

If we have m equations and n variables where m>n (more equations than variables), then system can be consistent if last m-n equations are linear combinations of previous ones.

For example:

x+y=1

x-y=1

3x+y=3

You can see that third equation is 2×first equation plus 1×second equation.

Solution of system is (x,y)=(1,0)

Result:

If we have m equation and n variables where m>n (more equations than variables), then system can be consistent if last m-n equations are linear combinations of previous ones.

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