MATLAB: Is 1/ones(3,1) OK while 1/ones(1,3) is not OK

Question

When I tried the code

1/ones(1,3)

matlab said this is invalid because the dimension is not matched.

Then I tried the code

1/ones(3,1)

this returns the result

ans =
     1     0     0

I don't know why the ans is like this.

Answer 1

Hi Yuki,

In the expression x = 1/ones(3,1) multiplying both sides on the right by ones(3,1) gives

x*ones(3,1) = 1.

The row vector x = [1 0 0] fills the bill, since

[1 0 0] x [1
           1  =    1.
           1]

Note that the answer is not unique, since

x = [0 1 0], x = [1/3 1/3 1/3] etc. all work just as well.

As to why ones(1,3) errors out, in that case you would have

x*ones(1,3) = 1.

If you review the rule for sizes of rows and columns in matrix multiplication, i.e. (mxn) x (nxq) = mxq, you will find that the eqn above does not work.