# Why is 1/ones(3,1) OK while 1/ones(1,3) is not OK?

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Yuki Koyama on 19 Sep 2019
Edited: David Goodmanson on 20 Sep 2019
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.
Stephen on 19 Sep 2019
"I don't know why the ans is like this."
Did you read the mrdivide documentation, to know what you are actually calculating?:

David Goodmanson on 19 Sep 2019
Edited: David Goodmanson on 20 Sep 2019
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.