Lesson Objectives
• Learn how to add matrices
• Learn how to subtract matrices

## How to Add and Subtract Matrices

In this lesson, we will learn how to add and subtract matrices. We can only add two matrices together if they are the same size. This means they have the same order or dimensions as we discussed in our last lesson. If we have a 3 x 4 matrix and another 3 x 4 matrix, we can add those matrices together. If we have a 2 x 3 and a 3 x 2, those can’t be combined with the addition operation. We would say that the operation is undefined or that the sum doesn't exist. Once you verify that the two matrices are the same size, we add two matrices together by adding the corresponding elements.
Example #1: Find A + B $$A=\left[ \begin{array}{cc}2&1\\ 3&5\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-1&3\\ 4&6\end{array}\right]$$ $$A + B=\left[ \begin{array}{cc}2 + (-1)&1 + 3\\ 3 + 4&5 + 6\end{array}\right]$$ $$A + B=\left[ \begin{array}{cc}1&4 \\ 7& 11\end{array}\right]$$ When we subtract one matrix from another, the same rule applies. Both matrices must be of the same order. Let's look at an example. $$A=\left[ \begin{array}{cc}2&1\\ 3&5\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-1&3\\ 4&6\end{array}\right]$$ $$A - B=\left[ \begin{array}{cc}2 - (-1)&1 - 3\\ 3 - 4&5 - 6\end{array}\right]$$ $$A - B=\left[ \begin{array}{cc}3&-2 \\ -1& -1\end{array}\right]$$

#### Skills Check:

Example #1

Find A + B $$A=\left[ \begin{array}{cc}9&5\\ 8&1\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-4&2\\ 3&7\end{array}\right]$$

A
$$A=\left[ \begin{array}{cc}7&3\\ 2&-1\end{array}\right]$$
B
Sum doesn't exist
C
$$A=\left[ \begin{array}{cc}5&7\\ 11&8\end{array}\right]$$
D
$$A=\left[ \begin{array}{cc}-2&4\\ 3&7\end{array}\right]$$
E
$$A=\left[ \begin{array}{cc}-4&7\\ 6&5\end{array}\right]$$

Example #2

Find A - B $$A=\left[ \begin{array}{cc}3&6\\ -8&-3\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-6&1\\ 2&-4\end{array}\right]$$

A
$$A=\left[ \begin{array}{cc}8&3\\ 2&-1\end{array}\right]$$
B
$$A=\left[ \begin{array}{cc}6&4\\ -3&2\end{array}\right]$$
C
$$A=\left[ \begin{array}{cc}-6&-2\\ 4&-5\end{array}\right]$$
D
$$A=\left[ \begin{array}{cc}9&5\\ -10&1\end{array}\right]$$
E
Sum doesn't exist