The set of all skew-symmetric n x n matrices is a subspace W of Mnxn(^) (see Exercise 28

Step 1 of 2

Let

Since  is a skew symmetric, so, for all.

So, if we know the entry above the diagonal, then we can get the element in the diagonal below of the diagonal.

So, the elements in the below diagonal are dependent on the elements of the above diagonal.

Look at the elements on the diagonal.

We have, so all the diagonal elements are zero.

So, the independent elements are the only elements strictly above the main diagonal.

So the setis the basis of