Matrix addition and subtraction

In this publication, we will look at how you can add two matrices or subtract one from the other. We will also give examples for a better understanding of the material presented.

sum of matrices

If we add the matrices A и B the same size, we get a matrix C the same size, the elements of which are equal to the sum of the corresponding elements of the original matrices.

A_mxn + B_mxn = C_mxn

Note: only the sum of matrices of the same size can be found.

Matrix addition properties

1. displacement law

A + B = B + A

2. association law

(A + B) + C = A + (B + C)

3. If a zero matrix is ​​added to the matrix, it will not change.

A + Θ = AWhere Θ is the null matrix.

4. If you subtract it from the matrix, you get a zero matrix.

A – A = Θ

Matrix difference

The difference of matrices can be represented as addition or multiplication of a matrix by a number.

С = A – B = A + (-B) = A + (-1) ⋅ B

In practice, this means that we simply find the difference between the corresponding elements of the matrices.

Note: subtraction is the same as addition, only matrices of the same size can be subtracted.

Examples of tasks

Task 1

Let’s find the sum of matrices A и Bpresented below.

Decision:

Task 2

Calculate the difference of matrices A и B.

Decision: