In the mathematics, we all are aware of one concept that is matrices. After all, in higher studies, it is a crucial chapter that contains a plenty of weightage. Matrices are one tool for organizing and displaying data (usually numbers). The following sorts of matrices are discussed, along with comparisons and contrasts between them: null, row, column, Sum of n Natural Numbers, diagonal, upper triangle, lower triangle, symmetric, asymmetric, involutory, idempotent, and orthogonal.
Matrix minors are calculated after excluding the row and column containing each element of the matrix. As a result of multiplying the minors of each element of the matrix, a new matrix is formed where you can include the Sum of Cubes of First n Natural Numbers. A matrix’s minor is commonly used to determine its determinant, adjoint, and inverse. In the following content, we will learn more about matrix minors.
Table of Contents
What Is Minor of Matrix?
The minor of a matrix corresponds to the matrix obtained after deleting the row and column in which that particular element is located. An element’s minor is shown here aij is denoted as Mij. The minor of matrix A, for example, is a12 when the first row and second column of the matrix are omitted, this is the part of the matrix that remains.
This matrix will be represented as:
How to Find Minor of Matrix?
The minor of a matrix can be found in three simple steps.
- Identify and exclude the row and column that contain the particular element within the matrix.
- Form a smaller matrix with the remaining elements to represent the minor of the particular element.
- Finally, form a new matrix containing the minor values of each element of the matrix by finding the determinant of the minor.
The minor of each element of the matrix can also be found similarly. By writing the minor of each element in the matrix array, we can form the minor of the matrix.
Applications of Minor of Matrix
The minor of the matrix can be used to find the cofactors of the elements, which can be used to find the adjoint and inverse of the matrix. In addition, the minor of the matrix is used to calculate the determinant of the matrix. Let discuss that how much type of matrices are available in this mathematical field.
What are Types of Matrices?
Mathematical, engineering, and scientific matrices are described in this article. The following are the most common linear algebra matrices:
- Row Matrix & Column Matrix
- Rectangular Matrix & Square Matrix
- Identity Matrix
- Singular Matrix & Nonsingular Matrix
- Hermitian Matrix & Skew-Hermitian Matrix
- Upper & Lower Triangular Matrices
- Symmetric Matrix and Skew Symmetric Matrix
- Zero Matrix
- Diagonal Matrix
- Orthogonal Matrix
The different types of matrices can be used to organize data by age group, person, company, month, etc. This information can then be used to solve many math problems and make decisions.
Addition and subtraction of matrices in matrix operations
Matrix operations like addition and subtraction are only possible when the number of rows and columns are equal. If so, the appropriate pieces can be added or subtracted. A, for instance, has two rows and two columns. If B has two rows and two columns, A and B can be added to or subtracted from. To reach the right solution, only combine or subtract the respective elements, being sure to keep them in the right order. If A and B are to be subtracted, each element of the array will have one B element removed from one A element.