Additive Inverse of a Matrix Tutorial

Matrix:

          In mathematics, the term Matrix is known as the rectangular arrangements of elements or entries arranged with in the square brackets. The elements may be like numbers, polynomials and expressions. In math, matrix can be represented by the capital alphabetical letters like A, B, C.

Tutorial:

          Tutorial is the process which gives the detailed solution to the problems.

Note:

Horizontal arrangements of elements are called as the row matrix.

E.g. `[[1,2,3]]` 

Vertical arrangements of elements are called as the column matrix.

E.g. `[[1],[2],[3]]`   

 

Operations of matrices:

 

 We can learn the following operations through online:

  • Addition
  • Subtraction
  • Matrix multiplication
  • Transpose
  • Inverse
  • Additive inverse
  • Multiplicative inverse

            Let us see how to calculate the Additive inverse of a matrix in this article.

 

Additive Inverse of a Matrix:

 

            Additive inverse of the matrix is obtained by changing the sign of the every entry or elements of the given matrix.The Additive inverse of the matrix A is wrriten as -A. The sum of the Given matrix A and the additive inverse of the matrix -A is always a zero matrix.

 

Examples on Additive Inverse of the Matrix:

 

      The following are the examples on additive inverse of the matrix tutorial:

Example 1:

                Let A = `[[9,8,7],[6,5,4],[3,2,1]]` . Find the Additive inverse of the matrix A.

Solution:

               Given: A = `[[9,8,7],[6,5,4],[3,2,1]]` .

Step 1:

               Change the sign of the every elements in the given matrix A.The resultant matrix is the additive inverse of the matrix.

                - A = `[[-9,-8,-7],[-6,-5,-4],[-3,-2,-1]]` .

Hence the additive inverse of the matrix A is `[[-9,-8,-7],[-6,-5,-4],[-3,-2,-1]]`  .

 

 

Example 2:

                Let A = `[[5,2,4],[5,2,4],[4,4,4]]` . Find the Additive inverse of the matrix A.

Solution:

               Given: A = `[[5,2,4],[5,2,4],[4,4,4]]`

Step 1:

               Change the sign of the every elements in the given matrix A.The resultant matrix is the additive inverse of the matrix.

                - A =`[[-5,-2,-4],[-5,-2,-4],[-4,-4,-4]]`

Hence the additive inverse of the matrix A is`[[-5,-2,-4],[-5,-2,-4],[-4,-4,-4]]`.

Example 3:

                Let A = `[[1,5,7],[2,9,6],[1,3,7]]` . Find the Additive inverse of the matrix A.

Solution:

               Given: A = `[[1,5,7],[2,9,6],[1,3,7]]` .

Step 1:

               Change the sign of the every elements in the given matrix A.The resultant matrix is the additive inverse of the matrix.

                - A = `[[-1,-5,-7],[-2,-9,-6],[-1,-3,-7]]` .

Hence the additive inverse of the matrix A is `[[-1,-5,-7],[-2,-9,-6],[-1,-3,-7]]` .

 

Practice Problem

     The following are the practice problem on Additive inverse of the matrix tutorial:

Problem 1:

               Let A = `[[9,8,9],[4,2,1],[5,5,6]]` . Find additive inverse of the matrix A.

Answer:

              - A = `[[-9,-8,-9],[-4,-2,-1],[-5,-5,-6]]` .

Problem 2:

               Let A = `[[9,0,2],[5,5,1],[4,3,3]]` . Find additive inverse of the matrix A.

Answer:

              - A =  `[[-9,0,-2],[-5,-5,-1],[-4,-3,-3]]` .