Using an array to solve a system of equations

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Discussion Overview

The discussion revolves around the use of an array, as opposed to a matrix, to solve a system of equations. Participants explore the definitions and distinctions between arrays and matrices, as well as methods for solving linear equations, including the potential application of Cramer's Rule and determinants.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to use an array to solve a system of equations, citing a specific example.
  • Another participant notes a lack of clarity between the terms "array" and "matrix," suggesting that they may be perceived as synonymous.
  • A third participant points out that solving the problem with a matrix inherently involves vectors, proposing that this may be what is meant by using an array.
  • There is a suggestion that "array" is more commonly a computer science term, with a two-dimensional array being analogous to a matrix.
  • A participant proposes the use of an augmented matrix as a potential method for solving the system of equations.
  • Questions are raised about the use of determinants in solving systems of linear equations, with some participants affirming their utility, particularly in conjunction with Cramer's Rule.
  • One participant mentions that Cramer's Rule is particularly effective for simple systems, especially when zeros are present in the matrix.
  • Another participant states a mathematical relationship involving the inverse of a matrix and its determinant, emphasizing the condition for the existence of the inverse.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the distinction between arrays and matrices, nor on the best method to solve the system of equations. Multiple competing views and methods remain present in the discussion.

Contextual Notes

There are unresolved assumptions regarding the definitions of arrays and matrices, as well as the applicability of various solving techniques like Cramer's Rule and the use of determinants.

barryj
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TL;DR
I was given a problem to use an array, not a matrix, to solve a system of equations. I have not heard of doing this and can not find any reference to how to do it.
I was given a problem to use an array, not a matrix, to solve a system of equations. I have not heard of doing this and can not find any reference to how to do it.

like... 2x+3y = 12, and 3x-4y = 14 How is this solved using an array or grid?
 
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Sorry, I can't help. I know a lot about this subject, but I don't know what the difference is between an array and a matrix. They are the same thing to me. Maybe you need to ask for clarification from your instructor?

As an aside, I spent some time in my career as an EE working with other good EEs that were educated in other countries. They knew what they were doing, because you probably wouldn't be working for our company if you didn't. But we were often confused by the jargon each used and their approach to problems. What ALWAYS worked was to go back to the basic physics, then everyone was on the same page.

PS: I think they are referring to Cramer's Rule; OTOH, no, IDK either.
 
It may not be obvious but when you solve that problem with a matrix, you are also using vectors. The statement of the problem is ## \begin{bmatrix} 2 & 3\\ 3 & -4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 12 \\ 14 \end{bmatrix}##. That might be what they are meaning.
 
barryj said:
I was given a problem to use an array, not a matrix
"Array" is more of a computer science term, where an ordinary array is a list, and a two-dimensional array corresponds to a matrix. AFAIK, "array" not so much a term used in mathematics.
 
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Does anybody ever use determinants to solve a system of linear equations?
 
gleem said:
Does anybody ever use determinants to solve a system of linear equations?
Yes. Cramer's rule, which is my first choice for simple systems. Especially if there are zeros in the matrix.

Also especially good if you only need the solution to one of the variables, which is never actually the case, in my experience.
 
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Obviously, if \mathbf{A}\mathbf{x}=\mathbf{y} then \mathbf{x}=\mathbf{A}^{-1}\mathbf{y} as long as \mathbf{A}^{-1} exists. Usually, this just means that det(\mathbf{A})\neq 0.
 

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