# Determine if following set is linearaly indepedent

• Mar 20th 2010, 09:39 PM
superdude
[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 http://img408.imageshack.us/img408/8518/onec.jpg and the rref of that is http://img683.imageshack.us/img683/4774/twok.jpg
so the last row of 0s confuses me. This means that the vectors are linearally dependent right?
• Mar 20th 2010, 10:40 PM
deniselim17
Quote:

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 http://img408.imageshack.us/img408/8518/onec.jpg and the rref of that is http://img683.imageshack.us/img683/4774/twok.jpg
so the last row of 0s confuses me. This means that the vectors are linearally dependent right?

Let \$\displaystyle a_{1}v_{1}+a_{2}v_{2}+a_{3}v_{3}=0\$.
From the rref you got, \$\displaystyle a_{1}=a_{2}=a_{3}=0\$.
So, l.i.
• Mar 21st 2010, 01:26 PM
superdude
Quote:

Originally Posted by deniselim17
Let \$\displaystyle a_{1}v_{1}+a_{2}v_{2}+a_{3}v_{3}=0\$.
From the rref you got, \$\displaystyle 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 \$\displaystyle a_1,a_2,a_3\$ eqaul 0 and there's no such thing as \$\displaystyle 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.