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.
Amxn + Bmxn = Cmxn
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:
А•В=?
4 -1 1
А= 1 1 -2
2 -3 -4