In mathematics, a matrix can be defined as a set of elements or numbers which are represented in various rows and columns resulting in the formation of a rectangular array. The inverse of a matrix is considered to be a different matrix which is multiplied by the matrix given resulting in giving a multiplicative identity. The multiplicative identity is one of the types of identities which states that, when a number is multiplied by 1, the resultant value remains the same. The matrix inverse is generally used to find or calculate the solutions of a linear equation. An equation that comprises only 1 term is defined as a linear equation. One unique fact about the inverse matrix is that it will only appear or exist if the value of the determinant of the matrix is zero. In this article, we will try to cover some basic aspects regarding the matrix inverse such as terms related to it, some basic rules, and do a brief analysis about it.
Invertible Matrix
In calculus, there are various types of matrices. One of them is the invertible matrix, it can be defined as the type of matrix for which the operation of matrix inversion exists, provided with suitable and requisite conditions. There are various applications of the invertible matrix in our day-to-day life. The significant applications are mentioned below:
- The invertible matrix comes into a three-dimensional form. We all know, the use of coding has become one of the most significant things in the modern world. This can be used to encrypt a message. The invertible matrix helps to encrypt a message as coding does.
- Have you heard about Cryptographer ?. They are considered to be the one who helps to keep the data private and safe. The invertible matrices are employed by the cryptographer to encrypt codes or data.
- The computer graphic uses the help of invertible matrices to render the picture that we see on our respective screens. They are present in the three-dimensional space.
Some Terms Related to the Inverse of Matrix
As mentioned above, the inverse of a matrix is considered to be a different matrix which is multiplied by the matrix given resulting in giving a multiplicative identity. There are various terms related to the inverse of a matrix. Some of them are mentioned below:
- Each and every element of a matrix is defined as minor. The minor in a matrix inverse is obtained when the columns containing the elements are eliminated.
- The value used for the representation of a matrix can be defined as the determinant of a matrix. It can be calculated by keeping a reference to any row or column given.
- Any matrix having the value of determinant zero is defined as the singular matrix. Similarly, when the value of the determinant is not equivalent to zero, it is referred to as the non-singular matrix.
Rule to be followed for the Columns and Rows of a Determinant
The following points analyze certain rules to be followed for the columns and rows of a determinant:
- If the values of the rows and columns are interchanged, the value of the determinant remains the same.
- When the rows and columns of a matrix are equal, the value of the determinant is equivalent to zero. Provided that: 2 columns and rows are equal.
- If the values of any two rows and columns are changed, the sign of the given determinant changes.
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