For a square matrix A which vectors are orthogonal to the ve

For a square matrix A, which vectors are orthogonal to the vectors in the null space, the vectors in Col(A) or the vectors in Row(A)?

Solution

Let null space vector of A be x

And Ri be ith row of A

So ith row element of Ax is Ri*x

Since , x is in null space so Ax=0

HEnce, Rix=0

HEnce, vectors in Row(A) are orthogonal to vectors in null space of A