How do matrices work?

  1. 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|
     
  2. jcsd
  3. TD

    TD 1,021
    Homework Helper

    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.
     
  4. 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 alot harder when n > 3 and m > 3.
     
  5. TD

    TD 1,021
    Homework Helper

    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?
     
  6. HallsofIvy

    HallsofIvy 40,544
    Staff Emeritus
    Science Advisor

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

    TD 1,021
    Homework Helper

    Which is why I said "simply put" :smile:
     
  8. radou

    radou 3,215
    Homework Helper

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

    AKG 2,585
    Science Advisor
    Homework Helper

    :surprised Have you looked?!
     
  11. Hurkyl

    Hurkyl 16,089
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
  12. HallsofIvy

    HallsofIvy 40,544
    Staff Emeritus
    Science Advisor

    Check the "Linear and Abstract Algebra" forum!
     
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