Add Matrices

Adding matrices

Matrix addition is done entry by entry. This means you add numbers that are in the same position in each matrix.

Method

1. Check the sizes of the matrices first. They must have the same number of rows and columns.
2. Add corresponding entries: top-left with top-left, top-right with top-right, and so on.
3. Write the result in the same matrix shape.

If the matrices are [ A=\begin{pmatrix}a&b\c&d\end{pmatrix},\quad B=\begin{pmatrix}e&f\g&h\end{pmatrix}, ] then [ A+B=\begin{pmatrix}a+e&b+f\c+g&d+h\end{pmatrix}. ]

Important idea

You do not multiply or combine entries from different positions. Only entries in matching positions are added.

Check your work

• Make sure every entry was added exactly once.
• Confirm the final matrix has the same shape as the originals.
• If negative numbers appear, watch the signs carefully.

Quick example

If [ \begin{pmatrix}2&-1\4&3\end{pmatrix}+\begin{pmatrix}5&6\-2&1\end{pmatrix}, ] then the sum is [ \begin{pmatrix}7&5\2&4\end{pmatrix}. ]

Work row by row or position by position to avoid mistakes.