I am trying to prove that $a_1$, $a_2$, $a_3$ are linearly independent.
I am asked to use vector product and prove that if $c_{1}a_{1} + c_{2}a_{2} + c_{3}a_{3} = 0$ then $c_1 = c_2 = c_3 = 0$
I am completely stuck on where to go with this problem. I would think that linearly independent then the null space of the space can only be equal to $0$. Would this prove it?
Best Answer
Dot through by a1. We get $$c_1(a1\cdot a1)=0$$ so $c_1=0$. The same holds for the other two constants. (I'm assuming that when you say orthogonal, you are not allowing any vectors to have zero magnitude.)