Skill: Add matrices

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For matrices with real-number entries, addition is defined only when the matrices have the same dimensions: each entry in the sum is obtained by adding entries in the corresponding row and column, so the result has the same dimensions. This combines aligned quantities entry by entry and differs from matrix multiplication; addition over more general number systems or abstract structures is not included.

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Detailed Explanation: Add matrices

To add two matrices, first check that they have the same dimensions. Then add the entries in matching positions. The sum has the same dimensions as the original matrices.

For example, add

A=\begin{bmatrix}2&-1&4\\0&3&5\end{bmatrix}, \qquad B=\begin{bmatrix}6&7&-2\\1&-3&8\end{bmatrix}.

Both matrices have $2$ rows and $3$ columns, so they can be added. Add corresponding entries:

A+B= \begin{bmatrix} 2+6&-1+7&4+(-2)\\ 0+1&3+(-3)&5+8 \end{bmatrix} = \begin{bmatrix} 8&6&2\\ 1&0&13 \end{bmatrix}.

Each entry in the answer comes from the same row and column in both matrices.

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