What is a Matrix in Math?

Matrix is a very useful topic that comes under linear algebra. It is an arrangement of elements, especially numbers, in a particular way. A matrix is a mathematical structure having rows and columns. The element aij of a matrix, say M refers to the element in the i-th row and j-th column.  The matrices are represented as square or rectangular parenthesis or in boxes. The horizontal and vertical lines of the matrix are represented as rows and columns. The numbers in the matrices are called entries or elements. The matrix size is specified in m rows and n columns like m-by-n matrices. The matrices are donated in the upper-case letters and the numbers are represented in the lower-case letters. 


A matrix can be represented in the following way: A = [ai, j] ∈ Rmxm.


For Example:


1) A 2 x 3 matrix has 2 rows and 3 columns:

\(\begin{array}{l}\begin{bmatrix} 1 & 2 &-1 \\ -6 & 7 & 3\end{bmatrix}\end{array} \)


2) A 4 x 4 matrix can be written as :

\(\begin{array}{l}\begin{bmatrix} 2 & 1 & \frac{3}{4} & 8\\ -1 & 6 & \frac{1}{2} & -1\\ 7 & 9 & \frac{5}{6}& 2\\ 1 & 2 & -\frac{1}{2} & 3 \end{bmatrix}\end{array} \)

Matrices do have a number of real-life applications which are discussed below:


1) Matrix plays an important role in computer science. It is useful in various computer programs, in projecting a three-dimensional image onto a two-dimensional plane, in coding and encrypting, in graphics and animation, etc.

2) Matrices are applicable in electric circuits, optics, quantum mechanics, estimation of battery power output and in other major calculations.

3) Matrices are quite useful in performing seismic surveys in geology.

4) Used in statistics while managing records, drawing graphs and in other calculations.

5) Play a vital part in robotic engineering in controlling movements of robots.

6) It has a great importance in economics in the calculation of production of goods effectively.


There are many more applications of matrices in various fields, such as :game theory, banking, mining, geometry, probability theory, etc.

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