Answer:
Step-by-step explanation:
Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar to the restriction on adding vectors, namely, only vectors from the same space R n can be added; you cannot add a 2‐vector to a 3‐vector, for example.) If A = [aij] and B = [bij] are both m x n matrices, then their sum, C = A + B, is also an m x n matrix, and its entries are given by the formula
Thus, to find the entries of A + B, simply add the corresponding entries of A and B.
Example 1: Consider the following matrices:
Which two can be added? What is their sum?
Since only matrices of the same size can be added, only the sum F + H is defined (G cannot be added to either F or H). The sum of F and H is
Since addition of real numbers is commutative, it follows that addition of matrices (when it is defined) is also commutative; that is, for any matrices A and B of the same size, A + B will always equal B + A.
