Question

hi can anyone tell me how to find the matrix whose nullspace is((2 1 0),(3 0 1))

Answer 1

Since (210) and (301) are in the null space, then

A(210)^T = A(301)^T =0

which means the rows of A are orthogonal to both of those vectors. So

A= (1 -2 -3
2 - 4 -6
3 -6 -9)

works.(There are an infinite set of possibilities, A needn't even be 3 by 3.)