Q1. - Algebra 2

Question

 Describe the conditions under which matrices can be added or subtracted.

Step-by-Step Solution

Answer

The conditions under which matrices can be added or subtracted are that two matrices A and B should be of the same dimensions $m\times n$ wherein each element is the sum or difference of the corresponding elements.

Step 1 - Define the first condition

Two matrices A and B should be added or subtracted if the dimensions of both the matrices are equal.

 

For example: $\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]$and $\left[\begin{array}{cc}3& -1\\ 2& 1\end{array}\right]$ both are the matrices of dimension $2\times 2$, therefore, operations of addition and subtraction can be applied to them.

Step 2 - Define the condition of matrix addition

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the sum of the corresponding elements.

 

For example: $\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]+\left[\begin{array}{cc}3& -1\\ 2& 1\end{array}\right]=\left[\begin{array}{cc}4& -1\\ 4& 2\end{array}\right]$

Step 3 - Define the condition of matrix subtraction

If A and B are two matrices of order $m\times n$, then the subtraction of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the difference of the corresponding elements.

 

For example: $\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]-\left[\begin{array}{cc}3& -1\\ 2& 1\end{array}\right]=\left[\begin{array}{cc}-2& 1\\ 0& 0\end{array}\right]$