Addition and subtraction of matrices.

When adding two or more matrices, their corresponding elements (components) are added together. The method of subtraction follows the same pattern as that of addition.

NB:

  • We can only add or subtract matrices if they are of the same order.
  • Such matrices are said to be compatible for addition or subtraction.
  • When the orders of the matrices are different, then addition or subtraction is impossible. Such matrices are said to be incompatible for addition or subtraction.

Example.

Given matrices

image 45

Work out

A + B

A – B

Solution

image 46

image 47

Example
Given that matrices C, D and E are:

image 48

Find:
a) C +(D – E)
b) C + D + E
c) C – (D + E)

Solution

image 49

Example
Given that:

image 50

Find;
i) P + Q
ii) Q – P

Solution
Here, matrix addition and subtraction is impossible because the two matrices are of different orders.