__4.3 Addition and Subtraction of Matrices__

**(A) Determining whether addition or subtraction can be performed on two given matrices**

**1.**Two matrices can be added or subtracted if both matrices have the same order.

**2.**The addition or subtraction of two matrices is performed by adding or subtracting the corresponding elements of the matrices.

**Example 1:**

State whether the following matrices can be added or subtracted. Give reason to your answer.

$\begin{array}{l}\text{(a)}\left(\begin{array}{l}2\\ 3\end{array}\right)\text{and}(1\text{}8)\\ \text{(b)}\left(\begin{array}{cc}1& 2\\ 7& 1\end{array}\right)\text{and}\left(\begin{array}{cc}10& 0\\ -3& -1\end{array}\right)\end{array}$

$\begin{array}{l}\text{(a)}\left(\begin{array}{l}2\\ 3\end{array}\right)\text{and}(1\text{}8)\\ \text{(b)}\left(\begin{array}{cc}1& 2\\ 7& 1\end{array}\right)\text{and}\left(\begin{array}{cc}10& 0\\ -3& -1\end{array}\right)\end{array}$

(c) (*p* 2 4) and (2 6 *q*)

Solution:

**(a) Cannot** because the matrices are not of the same order.

**(b) Can** because the matrices are of the same order.

**(c) Can** because the matrices are of the same order.

**Example 2:**

Express each of the following matrices as a single matrix.

$\begin{array}{l}\text{If}A=\left(\begin{array}{l}3\\ 2\end{array}\right)\text{and}B=\left(\begin{array}{l}5\\ 1\end{array}\right),\text{then}\\ \text{(a)}A+B=\left(\begin{array}{l}3\\ 2\end{array}\right)+\left(\begin{array}{l}5\\ 1\end{array}\right)\\ =\left(\begin{array}{l}3+5\\ 2+1\end{array}\right)\\ =\left(\begin{array}{l}8\\ 3\end{array}\right)\end{array}$