To find the sum of matrices, you simply add their corresponding entries together. This process is analogous to adding vectors.
Here's a breakdown:
-
Corresponding Entries: Each matrix has elements arranged in rows and columns. Corresponding entries are those that occupy the same row and column position in different matrices.
-
Addition: You add the values of the corresponding entries to get the corresponding entry in the resulting sum matrix.
Example
Here's an example, mirroring the one provided in the reference:
[
\begin{bmatrix}
6 & -3 \
2 & -7 \
0 & 4
\end{bmatrix} +
\begin{bmatrix}
5 & -6 \
-3 & -4 \
-2 & -4
\end{bmatrix} =
\begin{bmatrix}
6+5 & -3 + (-6) \
2 + (-3) & -7 + (-4) \
0 + (-2) & 4 + (-4)
\end{bmatrix} =
\begin{bmatrix}
11 & -9 \
-1 & -11 \
-2 & 0
\end{bmatrix}
]
In this example, the entry in the first row and first column of the resulting matrix (11) is the sum of the entries in the first row and first column of the two original matrices (6 + 5). The same logic applies to all other entries.
Key Considerations
-
Dimensions: Matrices can only be added if they have the same dimensions (i.e., the same number of rows and columns). You cannot add a 2x3 matrix to a 3x2 matrix, for instance.
-
Element-wise Operation: Matrix addition is an element-wise operation. This means each element in the resulting matrix is the result of an operation (addition, in this case) performed on the corresponding elements of the original matrices.
