We know that a set of vectors in a vector space is called a basis for if the following conditions are true.

1) spans

2) is linearly independent

I can't find the answer of my above mentioned question. All I can think of is this.

So in the above post are the row vectors of matrix and so spans the row space of which is :

Shouldn't because is the basis of row space of and for the fact that ?

So how and why

?

Can anyone kindly help me understand please?