Now if you say that your null space has to be equal to 0, you're saying that the only solution to this equation right here, the only scalars that satisfy this equation-- oh sorry, these aren't-- let me actually-- because I wrote the scalars as vectors-- so this guy right here, this statement right here, is equivalent to x1 times a1, plus x2 times a2, plus all the way to xn times an, is equal to the 0 vector.