Element by Element Division
Element by element division (the dot division) ./ works differently from Array multiplication / be careful not to confuse the two.
Division of Scalars
When we looked at subtraction we seen that 6 pens were used. If this is over a period of 3 months, we may want to know the amount of pens used each month so we can make a monthly order. To do this we can use division.
6 pens ./ 3 months = 6/3 pens/month = 2 pens/month
![\displaystyle \left[ {6\text{ pens}} \right]./\left[ {\text{3 months}} \right]=\left[ {6\text{ pens}/3\text{ months}} \right]=\left[ {2\text{ pens/month}} \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B6%5Ctext%7B+pens%7D%7D+%5Cright%5D.%2F%5Cleft%5B+%7B%5Ctext%7B3+months%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B6%5Ctext%7B+pens%7D%2F3%5Ctext%7B+months%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B2%5Ctext%7B+pens%2Fmonth%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ {6\text{ pens}} \right]./\left[ {\text{3 months}} \right]=\left[ {6\text{ pens}/3\text{ months}} \right]=\left[ {2\text{ pens/month}} \right]")
![\displaystyle \left[ 6 \right]./\left[ 3 \right]=\left[ {6/3} \right]=\left[ 2 \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+6+%5Cright%5D.%2F%5Cleft%5B+3+%5Cright%5D%3D%5Cleft%5B+%7B6%2F3%7D+%5Cright%5D%3D%5Cleft%5B+2+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ 6 \right]./\left[ 3 \right]=\left[ {6/3} \right]=\left[ 2 \right]")
i.e. we see that 2 pens are used per month.
To write this in MATLAB we would use
6./3
Note for a 1 by 1 scalar array division and element by element division are identical.
(Dot Division) of a Column Vector
If 6 pens and 3 pads were used up in 3 months then
![\displaystyle \left[ {\begin{array}{*{20}{c}} {6\text{ pens}} \\ {3\text{ pads}} \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} {3\text{ months}} \\ {3\text{ months}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3\text{ pens/month}} \\ {3/3\text{ pads/month}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {2\text{ pens/month}} \\ {2\text{ pads/month}} \end{array}} \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B6%5Ctext%7B+pens%7D%7D+%5C%5C+%7B3%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D.%2F%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B3%5Ctext%7B+months%7D%7D+%5C%5C+%7B3%5Ctext%7B+months%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B6%2F3%5Ctext%7B+pens%2Fmonth%7D%7D+%5C%5C+%7B3%2F3%5Ctext%7B+pads%2Fmonth%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%2Fmonth%7D%7D+%5C%5C+%7B2%5Ctext%7B+pads%2Fmonth%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ {\begin{array}{*{20}{c}} {6\text{ pens}} \\ {3\text{ pads}} \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} {3\text{ months}} \\ {3\text{ months}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3\text{ pens/month}} \\ {3/3\text{ pads/month}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {2\text{ pens/month}} \\ {2\text{ pads/month}} \end{array}} \right]")
![\displaystyle \left[ {\begin{array}{*{20}{c}} 6 \\ 3 \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} 3 \\ 3 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3} \\ {3/3} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 \\ 1 \end{array}} \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+6+%5C%5C+3+%5Cend%7Barray%7D%7D+%5Cright%5D.%2F%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+3+%5C%5C+3+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B6%2F3%7D+%5C%5C+%7B3%2F3%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+2+%5C%5C+1+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ {\begin{array}{*{20}{c}} 6 \\ 3 \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} 3 \\ 3 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3} \\ {3/3} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 \\ 1 \end{array}} \right]")
i.e. we see that 2 pens and 1 pad are used per month.
To write this in MATLAB we would use
[6;3]./[3;3]
(Dot Division) of Matrices
If the man in the red house used 6 pens and 2 pads up in a period of 3 months and the women in the green house used up 8 pens and 6 pads in a period of 4 months then
![\displaystyle \left[ {\begin{array}{*{20}{c}} {6\text{ pens}} & {\text{8 pens}} \\ {3\text{ pads}} & {4\text{ pads}} \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} {3\text{ months}} & {4\text{ months}} \\ {3\text{ months}} & {4\text{ months}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3\text{ pens/month}} & {8/4\text{ pens/month}} \\ {3/3\text{ pads/month}} & {4/4\text{ pads/month}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {2\text{ pens/month}} & {2\text{ pens/month}} \\ {1\text{ pads/month}} & {2\text{ pads/month}} \end{array}} \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B6%5Ctext%7B+pens%7D%7D+%26+%7B%5Ctext%7B8+pens%7D%7D+%5C%5C+%7B3%5Ctext%7B+pads%7D%7D+%26+%7B4%5Ctext%7B+pads%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D.%2F%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B3%5Ctext%7B+months%7D%7D+%26+%7B4%5Ctext%7B+months%7D%7D+%5C%5C+%7B3%5Ctext%7B+months%7D%7D+%26+%7B4%5Ctext%7B+months%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+%7B6%2F3%5Ctext%7B+pens%2Fmonth%7D%7D+%26+%7B8%2F4%5Ctext%7B+pens%2Fmonth%7D%7D+%5C%5C+%7B3%2F3%5Ctext%7B+pads%2Fmonth%7D%7D+%26+%7B4%2F4%5Ctext%7B+pads%2Fmonth%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%2Fmonth%7D%7D+%26+%7B2%5Ctext%7B+pens%2Fmonth%7D%7D+%5C%5C+%7B1%5Ctext%7B+pads%2Fmonth%7D%7D+%26+%7B2%5Ctext%7B+pads%2Fmonth%7D%7D+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ {\begin{array}{*{20}{c}} {6\text{ pens}} & {\text{8 pens}} \\ {3\text{ pads}} & {4\text{ pads}} \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} {3\text{ months}} & {4\text{ months}} \\ {3\text{ months}} & {4\text{ months}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3\text{ pens/month}} & {8/4\text{ pens/month}} \\ {3/3\text{ pads/month}} & {4/4\text{ pads/month}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {2\text{ pens/month}} & {2\text{ pens/month}} \\ {1\text{ pads/month}} & {2\text{ pads/month}} \end{array}} \right]")
![\displaystyle \left[ {\begin{array}{*{20}{c}} 6 & 8 \\ 3 & 4 \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} 3 & 4 \\ 3 & 4 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3} & {8/4} \\ {3/3} & {4/4} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 & 2 \\ 1 & 1 \end{array}} \right]](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%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.%2F%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+3+%26+4+%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+%7B6%2F3%7D+%26+%7B8%2F4%7D+%5C%5C+%7B3%2F3%7D+%26+%7B4%2F4%7D+%5Cend%7Barray%7D%7D+%5Cright%5D%3D%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D+2+%26+2+%5C%5C+1+%26+1+%5Cend%7Barray%7D%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "\displaystyle \left[ {\begin{array}{*{20}{c}} 6 & 8 \\ 3 & 4 \end{array}} \right]./\left[ {\begin{array}{*{20}{c}} 3 & 4 \\ 3 & 4 \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {6/3} & {8/4} \\ {3/3} & {4/4} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 2 & 2 \\ 1 & 1 \end{array}} \right]")
i.e. we see that the man uses 2 pens and 1 pad per month and the woman also uses 2 pens and 1 pad per month.
To write this in MATLAB we would use
[6,8;3,4]./[3,4;3,4]
