# Application of Matrices

The matrix in mathematics is a rectangular or square array of numbers or variables, arranged in the form of rows and columns. Individual items in a matrix are known as elements or entries.

The size of the matrix is determined by some its rows and columns. Matrix with ‘m’ rows and ‘n’ columns is read as ‘m*n’ matrix where m and n are its dimensions.

\(A=\begin{bmatrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12 \end{bmatrix}\)

For example, the matrix A mentioned above is a 3*4 matrix ,where 1,5,9,2,6 etc are its elements.

**Matrices Problems**

Two matrices can be added or subtracted element by element, provided both are of the same size.

Below image will help us in understanding the addition and subtraction operation on matrices,

But there is a rule for matrix multiplication, the number of columns in the first matrix should be equal to a number of rows in the second.

If A is a matrix of m*n and B is a matrix of n*p then their product matrix C=(A*B) will be m*p, whose elements are produced by the dot product of a corresponding row of A and a corresponding column of B.

**Application of matrices in engineering**

- Cryptography: Cryptography is a practice of hiding information for security purposes. Suppose you have a confidential data which has to be sent to someone. You can use a matrix to make the information to be readable to only the recipient.
- Fourier analysis
- Gauss theorem
- Finding electric currents using matrix equations
- Finding forces in the bridge