what is the physical application of matrices?

Answer 1

Matrices are just one way to express vectors and belong to a study of mathematics sometimes referred to as linear algebra. If you are able to proves some theorems about matrices *and* you are able to describe a physical phenomena (such as Newtonian mechanics) using vectors, then there are some conclusions you will try to draw about the physical phenomena.

An example may help. Grab two flashlights and walk into a dark room and turn them on. Now, shine the beam from one light into the other beam at right angles; the two beams cross each other but they don't interfere with each other: they don't cancel each other out, nor does one beam seem to "bounce" off the other. If you did this with streams of water from hoses the effect would be quite different. So, why don't light beams interfere with each other?

Well, if you assert that the mathematical description of a light beam is vector-like in nature, and you know that "linearly independent vectors" don't "affect" each other, you will be tempted to say (and be correct in saying it, too!) that the beams don't affect each other because they are linearly independent.

Maybe that will give you some idea of how matrices can be used. There are generalizations of a matrix that play crucial roles in some of the descriptions of relativity called tensors, and in quantum mechanics there are matrices with an infinite number of rows, or columns, or both!

HTH

Charles

Answer 2

matrices can be used for solving practical problems. like
ramesh brought 23 owls and 45 donkeys for Rs. 1235
rakesh brought 13 owls and 49 donkeys for Rs. 1239
find cost of 12 owls and 48 donkeys.
firstly equation is solved for 1 owl (say z) and 1 donkey (say y).
then 12z and 48y is calculated.

Answer 3

Solve equations.

A 2x2 matrix will solve a simultaneous equations with 2 variables.
.................
............................
A 7x7 matrix will solve a simultaneous equations with 7 variables.
A nxn matrix will solve a simultaneous equations with n variables.
A(n-1xn) matrix will solve a simultanious equations with n variables (propotionately only).