Tutorial Video
Element by Element Subtraction
Array subtraction works in an identical manner to element by element subtraction therefore it does not matter if we use - or .-.
Subtraction of Scalars
The items we illustrated are consumables. Taking the case of scalars, in this case only looking at pens, assuming we have 8 pens and use 6 of them up writing then after we put the 6 used up pens in the recycle bin we are left with:
8 pens - 6 pens = 2 pens
![\displaystyle \left[ {\text{8 pens}} \right]-\left[ {\text{6 pens}} \right]=\left[ {2\text{ pens}} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Ctext%7B8+pens%7D%7D+%5Cright%5D-%5Cleft%5B+%7B%5Ctext%7B6+pens%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B2%5Ctext%7B+pens%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
![\displaystyle \left[ 8 \right]-\left[ 6 \right]=\left[ 2 \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+8+%5Cright%5D-%5Cleft%5B+6+%5Cright%5D%3D%5Cleft%5B+2+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
To write this in MATLAB we would use
8-6
Subtraction of Column Vectors
If we started off with 8 pens and 5 pads and used up 6 pens and 3 pads then
Written as a column vector we will have:
![\displaystyle \left[ {\begin{array}{*{20}{c}} {\text{8 pens}} \\ {\text{5 pads}} \end{array}} \right]-\left[ {\begin{array}{*{20}{c}} {\text{6 pens}} \\ {3\text{ pads}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {2\text{ pens}} \\ {2\text{ pads}} \end{array}} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B%5Ctext%7B8+pens%7D%7D+%5C%5C+%7B%5Ctext%7B5+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D-%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B%5Ctext%7B6+pens%7D%7D+%5C%5C+%7B3%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B2%5Ctext%7B+pens%7D%7D+%5C%5C+%7B2%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
![\displaystyle \left[ {\begin{array}{*{20}{c}} 8 \\ 5 \end{array}} \right]-\left[ {\begin{array}{*{20}{c}} 6 \\ 3 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 \\ 2 \end{array}} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+8+%5C%5C+5+%5Cend%7Barray%7D%7D+%5Cright%5D-%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+6+%5C%5C+3+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+2+%5C%5C+2+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
To write this in MATLAB we would use
[8;5]-[6;3]
Subtraction of a Matrices
Okay so far, so good. Let's make things slightly more complicated again the man living in the red house has 8 pens and 5 pads and consumes 6 pens and 3 pads and the woman has 9 pens and 7 pads and consumes 8 pens and 4 pads. The man should therefore be left with 2 pens and 2 pads while the woman should be left with 1 pen and 3 pads
![\displaystyle \left[ {\begin{array}{*{20}{c}} {\text{8 pens}} & {9\text{ pens}} \\ {\text{5 pads}} & {\text{7 pads}} \end{array}} \right]+\left[ {\begin{array}{*{20}{c}} {\text{6 pens}} & {\text{8 pens}} \\ {\text{3 pads}} & {4\text{ pads}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {\text{2 pens}} & {\text{1 pens}} \\ {2\text{ pads}} & {3\text{ pads}} \end{array}} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B%5Ctext%7B8+pens%7D%7D+%26+%7B9%5Ctext%7B+pens%7D%7D+%5C%5C+%7B%5Ctext%7B5+pads%7D%7D+%26+%7B%5Ctext%7B7+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%2B%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B%5Ctext%7B6+pens%7D%7D+%26+%7B%5Ctext%7B8+pens%7D%7D+%5C%5C+%7B%5Ctext%7B3+pads%7D%7D+%26+%7B4%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B%5Ctext%7B2+pens%7D%7D+%26+%7B%5Ctext%7B1+pens%7D%7D+%5C%5C+%7B2%5Ctext%7B+pads%7D%7D+%26+%7B3%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
![\displaystyle \left[ {\begin{array}{*{20}{c}} 8 & 9 \\ 5 & 7 \end{array}} \right]+\left[ {\begin{array}{*{20}{c}} 6 & 8 \\ 3 & 4 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 & 1 \\ 2 & 3 \end{array}} \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+8+%26+9+%5C%5C+5+%26+7+%5Cend%7Barray%7D%7D+%5Cright%5D%2B%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+6+%26+8+%5C%5C+3+%26+4+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+2+%26+1+%5C%5C+2+%26+3+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0&c=20201002)
To write this in MATLAB we would use
[8,9;5,7]-[6,8;3,4]
