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Current Location > Math Formulas > Linear Algebra > Matrix Addition

Matrix Addition

Two matrices may be added only if they have the same dimension; that is, they must have the same number of rows and columns. Addition is accomplished by adding corresponding elements.

For example, consider matrix A and matrix B.

Both matrices have the same number of rows and columns (3 rows and 3 columns), so they can be added. Thus,

And finally, note that the order in which matrices are added is not important, thus:
A + B = B + A.

Example 1: Add the two given matrices:

Solution: Here the dimension of both the matrices is same, so we add the same.

Example 2: What is the resultant when we add the two given matrices?

Solution: As the dimension of both the matrices is same, we can add the corresponding entries to get the sum.

Example 3:
Solution: