How is matrix addition performed?

• A. By multiplying corresponding elements from different matrices
• B. By adding corresponding elements from equal-sized matrices
• C. By averaging corresponding elements from two matrices
• D. By adding all elements together

Answer: (B)

Matrix addition is performed by adding the corresponding elements from two matrices that have the same dimensions. This means that if you have two matrices, each with the same number of rows and columns, you combine them element-wise. For instance, if you have matrix A with elements a_{ij} and matrix B with elements b_{ij}, the resulting matrix C will have elements c_{ij} = a_{ij} + b_{ij}. This process applies to each pair of corresponding elements, ensuring that the dimensions of both matrices are identical.

Choosing the other options would not accurately describe how matrix addition works. For instance, multiplying corresponding elements (as mentioned in the first option) does not define matrix addition. Averaging elements (as suggested in the third option) would produce a different result entirely and is not part of the standard addition process. Lastly, the idea of adding all elements together (in the fourth option) implies a single scalar result rather than creating a new matrix structured like the originals. Thus, option B correctly encapsulates the fundamental rule of matrix addition.