Using an array to solve a system of equations

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?

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.

Maybe you are meant to use an augmented matrix:
https://tutorial.math.lamar.edu/classes/alg/augmentedmatrix.aspx

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.

Obviously, if [itex]\mathbf{A}\mathbf{x}=\mathbf{y} [/itex] then [itex]\mathbf{x}=\mathbf{A}^{-1}\mathbf{y} [/itex] as long as [itex]\mathbf{A}^{-1} [/itex] exists. Usually, this just means that [itex]det(\mathbf{A})\neq 0 [/itex].