use of matrices?

Answer 1

they are used to Solve equations with many unknowns ..

but you must have the Same number of Equations as the Unknowns..

so if you have 10 unknowns to solve them (to know what are these numbers) you need 10 DIFFERENT equation...

that's it for now..
hope you got what you need..

Answer 2

In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on two parameters. Matrices can be added, multiplied, and decomposed in various ways, marking them as a key concept in linear algebra and matrix theory.

Applications:

Transportation:

If one is given a list of cities (or destinations, nodes, etc) and is told that there are flights (or roads, connections, etc) from city a to city b, then one can build a square matrix with the cities indexing each side of the matrix. So each entry M[a,b] = 1 if there is a connection from a to b. If there is a reverse connection from b to a then also M[b,a] = 1. In many instances the connection a to b might not be bidirectional, ie M[a,b] = 1 does not necessarily imply that M[b,a] = 1. If there is no connection from a to b then M[a,b] = 0.

By multiplying the matrix M by itself to obtain M2, then M2 will indicate if two cities a and b can be reached by 1 or more layovers. That is, if for example M[a,b] = 0, but M2[a,b] = 1, then a and b are connected via a third city c, a layover between a and b. If M2[a,b] = n then a and b are connected via n layovers.

It is very useful in operation management.

Answer 3

The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850.


"Matrix" is the Latin word for womb, and it retains that sense in English. It can also mean more generally any place in which something is formed or produced

The orgins of mathematical matrices lie with the study of systems of simultaneous linear equations. An important Chinese text from between 300 BC and AD 200, Nine Chapters of the Mathematical Art (Chiu Chang Suan Shu), gives the first known example of the use of matrix methods to solve simultaneous equations.

In the treatise's seventh chapter, "Too much and not enough," the concept of a determinant first appears, nearly two millennia before its supposed invention by the Japanese mathematician Seki Kowa in 1683 or his German contemporary Gottfried Leibnitz (who is also credited with the invention of differential calculus, separately from but simultaneously with Isaac Newton).

More uses of matrix-like arrangements of numbers appear in chapter eight, "Methods of rectangular arrays," in which a method is given for solving simultaneous equations using a counting board that is mathematically identical to the modern matrix method of solution outlined by Carl Friedrich Gauss (1777-1855), also known as Gaussian elimination

The term "matrix" for such arrangements was introduced in 1850 by James Joseph Sylvester.

Sylvester, incidentally, had a (very) brief career at the University of Virginia, which came to an abrupt end after an enraged Sylvester hit a newspaper-reading student with a sword stick and fled the country, believing he had killed the student!

Since their first appearance in ancient China, matrices have remained important mathematical tools. Today, they are used not simply for solving systems of simultaneous linear equations, but also for describing the quantum mechanics of atomic structure, designing computer game graphics, analyzing relationships, and even plotting complicated dance steps!



The elevation of the matrix from mere tool to important mathematical theory owes a lot to the work of female mathematician Olga Taussky Todd (1906-1995), who began by using matrices to analyze vibrations on airplanes during World War II and became the torchbearer for matrix theory.

http://www.ualr.edu/lasmoller/matrices.html

Answer 4

Think of a system of linear equation. When you try to solve them by operations, you are manipulating the co-efficients. Why not get the variables out of the way--it makes it easier!

Answer 5

The system of matrix allow the question to be solved using a series of simpler methods. the number of calculation increases but the difficulty of each of them decreases.

Answer 6

You use Matrix (assuming is about Maths) to solve eqns of more than 2 unknown variables, it could be more than 2 eqns to solve. For example we can use Matrix to solve such problem Solve:
2x+3y=7
5x-y=18
x+y=4

Answer 7

are u asking what r they used for? or how to solve them?


i am not sure. but i think it is just an easier way to do many of the same calculations with different numbers.

Answer 8

solving simulatious equation of higher order
differential variables n equations
three dimensional geometry
vectors and eigen variables
scientically..caluclations relating to simple harmonic motions ....r
only some of many

Answer 9

Computer programing, lists, composite material engineering. There are uses so just study.

Answer 10

there are many....
for example, vector operations are just one.