Add and Subtract Matrices

Introduction about matrices:

Matrix has a list of data. In matrix is a rectangular arrangement of the elements. The elements are shown in the rows and the columns. Array elements are put in the parenthesis or square brackets. In matrix is represented by capital letters for example A, B, C…… We can do addition, subtraction and multiplication in matrices. In this article we shall discuss about the addition and subtraction process of matrix.

Addition of Matrices:

If we add two matrices add the first element of first matrix with first element of second matrices repeat the process for all the elements. An addition matrix is similar to normal addition.

If we add two matrices they are in the same order. For example matrix A present in 3 `xx` 3 structure the matrix B also present in 3 `xx` 3 structure else ( if the matrix B present in 2 `xx` 3 form or etc) we cannot add the matrices.

Example sums for addition of matrices:

Example:

Add the following two matrices

A= `[[2,-3],[-5,4]]`

B= `[[8,2],[-1,7]]`

A + B=?

Solution:

Given

A= `[[2,-3],[-5,4]]`

B= `[[8,2],[-1,7]]`

A + B= `[[2,-3],[-5,4]]`+ `[[8,2],[-1,7]]`

A + B= `[[2+8,-3+2],[-5-1,4+7]]`

A + B= `[[10,-1],[-6,11]]`

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Subtraction of Matrices:

Subtraction of matrices are some more different from normal substitution. Subtraction of matrices follows some rules. The following steps are used to subtract the matrices.

Step 1:

First create the negative matrix for subtrahend matrix.

Step 2:

Add the negative matrix (previous step result) with next matrix

For example if we do the process A-B matrix first discover the negative of B matrix and then add –B matrix with A matrix  like A + (-B)

Example Problems for Subtraction of Matrices:

Example:

Subtract the following two matrices

A = `[[-5,-8],[4,6]]`

B= `[[2,5],[-8,-7]]`

A-B=?

Solution:

Given

A = `[[-5,-8],[4,6]]`

B= `[[2,5],[-8,-7]]`

Step 1:

First create the negative matrix for subtrahend matrix.

- B = - `[[2,5],[-8,-7]]`

- B = `[[-2,-5],[8,7]]`

Step 2:

Add the negative matrix (previous step result) with next matrix

A + (-B) =  `[[-5,-8],[4,6]]` + `[[-2,-5],[8,7]]`

A + (-B) = `[[-5 + (-2),-8+(-5)],[4+8,6+7]]`

A + (-B) = `[[-7,-13],[12,13]]`