What is the explanation behind matrices in Algebra?

[eNathan]

I am currently working on Matrices in my Algebra. I have not seen much talk about it on these forums. Can somebody please explain it? They look like

|5 6 2 0|
|5 0 4 8|
|5 5 7 6|
|8 4 6 1|

 

[TD]

Simply put, a matrix is a table of m columns and n rows in which you place numbers.
The applications are very different, solving lineair systems is a very common one.

 

[eNathan]

What good do matrices do in the real world? I.E. what are they used for?

How do you compute matrix set? I have a question here that asks "the cofactor of a_22 = 5 is?" :uhh: it all seems confusing. I learned about 3*3 matrices a few months ago, but I heard that they get a lot harder when n > 3 and m > 3.

 

[TD]

As I said, one of the most common (and important) uses is that you can use matrixes to solve systems of lineair equations (by, for example, using gaussian elimination or Cramer's rule for square matrices).

To fully understand minors/cofactors, you'll need to know what determinants are, do you?

 

[HallsofIvy]

Simply put, a matrix is a table of m columns and n rows in which you place numbers.
The applications are very different, solving lineair systems is a very common one.

That's an "array" or a "tableau". Any definition of matrices has to include the ability to add and multiply them.

 

[TD]

Which is why I said "simply put"

 

[radou]

You can also think of a matrix as an ordered data structure. A matrix often describes a physical state or property of matter.

 

[An Anomaly]

What good do matrices do in the real world? I.E. what are they used for?

Too many things to list. From using them with kirchhoffs laws, to the cross product rule, to determining the amount of solutions within the system of equations.

 

[AKG]

I have not seen much talk about it on these forums.

Have you looked?!

 

[Hurkyl]

Matrices are important because a great many things can be represented as matrices.

The first example people learn is that of a linear transformation, when dealing with vector spaces. A linear transformation T is a function satisfying:

T(αx + βy) = αT(x) + βT(y)

where α and β are scalars. (If the scalars are, for example, real numbers, we say that this is an R-linear transformation)

Linear transformations are important because they respect the indicated algebraic operations.

 

[HallsofIvy]

I have not seen much talk about it on these forums.

Check the "Linear and Abstract Algebra" forum!