Question

for a square 100 by 100 matrix A and the vector x (x1,...,x100) where Ax is the 0 vector. where the matrix A is singular. how can i now some linear combination of either the 100 rows or the 100 columns. my guess is that either could be the 0 vector, but i don't really know why. this is relating to problem set 2.2 question 32 a and b in the fourth edition textbook.