GCSE Mathematics/Matrices

Adding/subtracting matrices

When adding or subtracting matrices you should add/subtract numbers in the same position, like this:

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

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

Matrices can only be added/subtracted if they are of the same size.

Multiplying matrices

When multiplying matrices by a number, you should multiply all the numbers inside them by that number, for example:

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