Solution Set for 4 Equations in 3 Unknowns

[EV33]

Homework Statement

Determine all possibilities for the solution set (from among infinitely many solutions, a unique solution, or no solution) of the system of linear equations.

A system of 4 equations in 3 unknowns

Homework Equations

None.

The Attempt at a Solution

This is more of a word problem.

Under the assumption that "4 equations in 3 unknown's means a 4X3 Matrix then I would say that there are an infinite amound of solutions because 4X3 matrix could be filled with an infinite amount of options.

Is that correct?

 

[rock.freak667]

With n unknowns you need at least n equations to get a unique solution.

 

[Dick]

If the first equation is a=0 and the second equation is a=1, I doubt there are an infinite number of solutions. Just saying "a 4x3 matrix could be filled with an infinite number of options" means you are thinking about this really vaguely. Try and be more concrete. Any of those options is actually possible. Try and give an example of each.

 

[Dick]

With n unknowns you need at least n equations to get a unique solution.

"4" equations. "3" unknowns. There are plenty of equations.

 

[jegues]

4 equations in 3 unknown's means a 4X3 Matrix

Not necessairly, you didn't specify whether you were looking at the augmented matrix or the coefficient matrix. Consider the rank of the matrix(either augmented or coefficient), this should help you determine the number of parameters(free variables) and point you towards a conclusion.

 

[rock.freak667]

"4" equations. "3" unknowns. There are plenty of equations.

well that was my point. Though I probably worded it badly.

 

[Altabeh]

A system of 4 equations in 3 unknowns

This is an overdetermind system of linear equations which if it happens to have a solution, it is unique. Otherwise it won't have any exact solution assuming no two eauations coincide. You can use methods like "square least" to get the nearest set of solutions that is not always guaranteed to be a good approximation, but still a very useful and reliable one.

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