Thread: Determine if following set is linearaly indepedent

1. [STILL NEED HELP] Determine if following set is linearaly indepedent

Determine if the following set is linearly independent or linerly dependent.
v_1=[1;2;1;-2] v_2=[2;1;-3;-1] v_3=[1;2;6;-5]

so I create the matrix and the rref of that is
so the last row of 0s confuses me. This means that the vectors are linearally dependent right?

2. Originally Posted by superdude
Determine if the following set is linearly independent or linerly dependent.
v_1=[1;2;1;-2] v_2=[2;1;-3;-1] v_3=[1;2;6;-5]

so I create the matrix and the rref of that is
so the last row of 0s confuses me. This means that the vectors are linearally dependent right?

Let $a_{1}v_{1}+a_{2}v_{2}+a_{3}v_{3}=0$.
From the rref you got, $a_{1}=a_{2}=a_{3}=0$.
So, l.i.

3. Originally Posted by deniselim17
Let $a_{1}v_{1}+a_{2}v_{2}+a_{3}v_{3}=0$.
From the rref you got, $a_{1}=a_{2}=a_{3}=0$.
So, l.i.
does l.i. stand for linearally independent?

I'm really getting confused

Is it because all the nescecary constants $a_1,a_2,a_3$ eqaul 0 and there's no such thing as $a_4$? and that makes it linearally independent?

also, a more general question: to find if a set of vectors is a basis, one must determine if they are linearally independent and span the given vector space. Since the procedure is the same for both of them, doesn't it mean that if the vectors span the given vector space it also implies that they are linearally independent, and vice versa? I say this because to show the vectors span R^n then the procedure is to try to put them in rref form. To show that they are linearally independent they need to be put in rref form.