Question Regarding Division Operation

Why does a/b gives a 3x3 matrix instead of giving an error for the following example? What Operation is it Performing?

a = [1 2;3 4;5 6] and b = [3 4; 5 6;7 8]

a./b = [0.33 0.5;0.60 0.66;0.7143 0.75] and a/b = [1.5 0 -0.5;1 0 0;0.5 0 0.5]

Answer 1

[James Tursa]

Using the ./ operator with the dot does element-wise division. Using / without the dot does matrix linear equation solving. So this operation:

x = a/b

is the solution to the following equation

x*b = a

I.e., conceptually you divide both sides of this equation on the right by b to get the solution above. This is simply a set of linear equations that MATLAB is solving using the "backslash" or "forwardslash" operator. E.g.,

>> a = [1 2;3 4;5 6]
a =
     1     2
     3     4
     5     6
>> b = [3 4; 5 6;7 8]
b =
     3     4
     5     6
     7     8
>> x = a/b
x =
    1.5000         0   -0.5000
    1.0000         0         0
    0.5000         0    0.5000
>> x*b
ans =
    1.0000    2.0000
    3.0000    4.0000
    5.0000    6.0000