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.
![\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
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
(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
