Matrix subtraction

We can only subtract matrices with the same order.

Subtracting matrices

To subtract matrices, simply subtract the corresponding elements from each matrix.

Find where and

• We subtract the corresponding elements:
  • Top-left:
  • Top-right:
  • Bottom-left:
  • Bottom-right:
• So,
• Answer:

Find the value of where and

• We subtract the corresponding elements:
  • Top-left:
  • Top-right:
  • Bottom-left:
  • Bottom-right:
• So,
• Answer:

Find the value of where , and

• First, we find :
  • Top-left:
  • Top-right:
  • Bottom-left:
  • Bottom-right:
• So
• Then we do that value minus :
  • Top-left:
  • Top-right:
  • Bottom-left:
  • Bottom-right:
• So,
• Answer:

Commutative

• Matrix subtraction is not commutative, which means that (in general).
• FOr example, if and , then
• The results will always be the negative variant of each other.

Associative

• Matrix subtraction is also not associative, which means that (in general).
• For example, if , and , then
• The results are different, so it’s not associative.

Distributive

• Matrix subtraction is distributive over matrix addition, which means that .
• For example, if , and , then
• The results are the same, so it’s distributive.