Matrix dimensions and compatibility
To work with matrices correctly, first identify the size of each matrix. A matrix with 2 rows and 3 columns is called a 2 × 3 matrix. The dimensions tell you whether an operation is possible and what size the result will have.
1) Check compatibility
- Addition or subtraction: the matrices must have the same dimensions.
- Multiplication: the number of columns in the first matrix must match the number of rows in the second matrix.
2) Find the result size
- For addition/subtraction, the result has the same dimensions as the matrices.
- For multiplication, if an m × n matrix is multiplied by an n × p matrix, the product is an m × p matrix.
3) Simplify carefully
When the exercise asks for the final answer, write the resulting dimensions clearly and reduce any arithmetic if you compute entries.
4) Quick check
Before finishing, verify:
- the dimensions you identified are correct,
- the operation is allowed,
- the final size matches the compatibility rule.
If an operation is not allowed, the correct response is to say so rather than forcing a result.