In academics, we have studied various important concepts in Maths. Some of the topics are not only important for examinations but also have a wide range of applications in various fields. Probability, differentiation and integration, statistics, matrices, and so on are employed in many applications that we are using in our day-to-day life activities. Here we are going to discuss the applications of one such important concept called “Matrix” in detail.
Before discussing the application of the matrix, let us have a brief look at the concept of a matrix. A matrix is a rectangular array of numbers arranged in rows and columns. Each value present in the matrix is known as elements. The elements which are present horizontally are called rows, and the elements present vertically are called the columns. The dimension of the matrix can be measured in terms of rows and columns. Based on the size of the matrix, the matrix dimension should be 2×2 matrix, 3×3 matrix, nxn matrix.
Like arithmetic operations, the matrix can be added, subtracted or multiplied. Apart from these operations, the other operations like transpose, adjoint, inverse of a 3×3 matrix, 2×2 matrix can also be performed.
Applications of Matrices
Matrix has many applications in the field of Science, Technology, and so on. Now, let us discuss the applications one by one.
In the earlier days, cartoons, animations were created by hand. But, nowadays they are done using computer graphics. The graphic software uses the matrix to perform the linear transformations into the images. It helps to project the 3D images in the two-dimensional plane. The rows and columns in the matrix represent rows and columns of the pixels. The numerical values represent the pixel colour value. In video games, the matrix is used to manipulate the points.
We know that wireless communication plays a vital role in the telecommunication industry. For signal estimations and detection of problems in the wireless signals, the matrix plays a key role. Matrix helps to represent and process the digital images. Matrices are used to design the adaptive filter and used in sensor array signal processing.
Matrix is an important tool to solve many problems in business and economics, which are related to maximizing the profit or minimizing the loss. To rectify the problems, determinants, and matrices are used to find the variance and covariance. Generally, Cramer’s rule is used to find the solution of linear equations.
Cryptography is the method of the encryption of the data. Once the data is encrypted, only the relevant person can decrypt the data. The process of encryption is performed with the help of an invertible key. It is done with the help of matrices. Generally, the message is converted into the sequence of numbers. The filtering techniques which are used in the encryption process depend on the matrix multiplication, and we have to select a matrix, whose determinant is a non-zero value.
Apart from these applications, matrices are used to find the area of a triangle, collinear points, and in many aspects of engineering, physics, and so on. To know more interesting information, subscribe to BYJU’S YouTube Channel.