Solving Linear Systems with "m Equations & n Unknowns

In summary, the conversation discusses the terminology and notation used to describe a linear system with "m equations in n unknowns." The participants conclude that both forms, "m equations in n unknowns" and "n unknowns in m equations," are equivalent and can be used interchangeably. However, there is a convention to use the former in English and the latter in some other languages.
  • #1
delgeezee
12
0
My book describes a linear system with "m equations in n unknowns."

Maybe this is a subtle detail but this confuses me. Shouldn't it be the other way around, "n unknowns in m equations?"
 
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  • #2
Re: terminology

It makes no difference, so long as m and n are defined.
 
  • #3
Re: terminology

They both mean the same thing as far as I can tell. I think this may be a language problem, the first form might be more natural in english whereas the other sounds more natural in other languages (for instance french).​
 
  • #4
Re: terminology

I'd write the first form as "m equations with n unknowns."
Anyway, the two forms mean the same thing.
 
  • #5
Re: terminology

Like others said the variable names can be whatever you want to use, but standard convention is that a matrix of size $m \times n$ corresponds to a linear system of equations, which means that there are $m$ rows and $n$ columns. That corresponds to $m$ equations and $n$ variables.
 

FAQ: Solving Linear Systems with "m Equations & n Unknowns

What is a linear system with "m Equations & n Unknowns"?

A linear system with "m Equations & n Unknowns" is a collection of m linear equations with n unknown variables. These equations can be solved simultaneously to find values for each of the unknown variables that satisfy all of the equations.

Can a linear system with "m Equations & n Unknowns" have multiple solutions?

Yes, a linear system with "m Equations & n Unknowns" can have multiple solutions. These solutions can be represented as ordered pairs or vectors, depending on the number of variables in the system.

What is the most common method for solving linear systems with "m Equations & n Unknowns"?

The most common method for solving linear systems with "m Equations & n Unknowns" is the Gaussian elimination method. This involves using elementary row operations to reduce the system to row echelon form, and then using back substitution to find the values of the unknown variables.

Can a linear system with "m Equations & n Unknowns" have no solution?

Yes, a linear system with "m Equations & n Unknowns" can have no solution. This occurs when the equations are inconsistent, meaning there is no combination of values for the unknown variables that satisfy all of the equations.

What is the importance of solving linear systems with "m Equations & n Unknowns" in science?

Solving linear systems with "m Equations & n Unknowns" is important in science because many real-world problems can be represented as systems of linear equations. These problems can range from determining the optimal solution to a system of equations to modeling real-life scenarios in fields such as physics, engineering, and economics.

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