Lesson 5 of 8
Add and subtract matrices
Add or subtract two matrices of the same size, one position at a time.
The idea
Matrices are added the same way as vectors: entry by entry. The entry in row 1, column 1 of A is added to the entry in row 1, column 1 of B, and so on for every position.
That only makes sense when both matrices have the same size, so every entry has a partner.
Worked example: adding
Find AplusB.
Check the sizes
A and B are both 2×2, so A + B is defined and is also 2×2.
Add matching entries
A plus B equals a matrix with row 1: 1 plus 5, 4 plus 0; row 2: 2 plus 1, 3 plus 2Simplify
A plus B equals a 2 by 2 matrix, row 1: 6, 4; row 2: 3, 5
Worked example: subtracting
For A − B, subtract each entry of B from the matching entry of A. Keep the order: A’s entry comes first.
Find AminusB.
Check the sizes
A and B are both 2×2, so A − B is defined and is also 2×2.
Subtract matching entries
A minus B equals a matrix with row 1: 7 minus 2, 5 minus 3; row 2: 4 minus 4, 9 minus 1Simplify
A minus B equals a 2 by 2 matrix, row 1: 5, 2; row 2: 0, 8
When you cannot add
These two matrices cannot be added, because one is 2×3 and the other is 2×2. Some entries would have no partner.
Once 2×2 feels comfortable, practice will also include 2×3 matrices. The rule is exactly the same.
Common mistakes
- Pairing the wrong entries. Only entries in the same row and the same column go together.
- Subtracting in the wrong order. In A − B, take B’s entry away from A’s.
- Sign slips with negatives. 4 − (−2) = 6.