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.

1. 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