Study of mathematics online.
Study math with us and make sure that "Mathematics is easy!"

Matrix addition and subtraction

You can add and subtract the matrix of the same size as a resulting you get the matrix of the same size.

Definition.
Addition of matrix (sum of matrix) A + B is operation of a finding of a matrix C, entry of which are equal to the sum of all corresponding entry of matrix A and B, can be defined as:

сij = aij + bij

Definition.
Subtraction of matrix (difference of matrix) A - B is operation of a finding of a matrix C, entry of which are equal to a difference of all corresponding entry of matrix A and B, can be defined as:

сij = aij - bij

Properties of matrix addition and subtraction

• Associativity: (A + B) + C = A + (B + C)
• A + Θ = Θ + A = A, where Θ - zero matrix
• A - A = Θ
• Commutativity: A + B = B + A

Examples of matrix addition and subtraction

Example 1.
 Find the sum of matrices A = 4 2 and B = 3 1 . 9 0 -3 4

Solution:

 A + B = 4 2 + 3 1 = 4 + 3 2 + 1 = 7 3 9 0 -3 4 9 + (-3) 0 + 4 6 4
Example 2
 Find the difference of matrices A = 4 2 and B = 3 1 . 9 0 -3 4

Solution:

 A - B = 4 2 - 3 1 = 4 - 3 2 - 1 = 1 1 9 0 -3 4 9 - (-3) 0 - 4 12 -4
Example 3
 Find the matrix С = 2A + 3B, if A = 4 2 and B = 3 1 . 9 0 -3 4 4 -6 9 1

Solution:

 C = 2A + 3B = 2 4 2 + 3 3 1 = 2·4 + 3·3 2·2 + 3·1 = 17 7 9 0 -3 4 2·9 + 3·(-3) 2·0 + 3·4 9 12 4 -6 9 1 2·4 + 3·9 2·(-6) + 3·1 35 -9

Add the comment

 0