What operation involves adding corresponding elements of two matrices?

Matrix addition involves adding corresponding elements of two matrices together to create a new matrix. For two matrices to be added, they must have the same dimensions, meaning the number of rows and columns must match. Each element from the first matrix pairs with the corresponding element from the second matrix, and these pairs are summed to form the elements of the resulting matrix. This operation is defined as follows: if you have two matrices A and B, the resulting matrix C will have each element C[i][j] equal to A[i][j] + B[i][j].

For example, if you have two matrices:

[ A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} ]

[ B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix} ]

The result of the addition will be:

[ C = \begin{pmatrix} 1+5 & 2+6 \ 3+7 & 4+8 \end{pmatrix} = \begin{pmatrix} 6 & 8 \ 10 & 12 \end{pmatrix} ]

This operation is crucial in