
Two quick questions
Question 1
If I have matrix v1 = (1,1,2) v2 = (4,6,7) and v3 (1,1,k)
Am I right in saying that if k = 2, v1,v2,v3 is linearly dependent, because v3 = 1(v1)?
And following that, if I had to write one vector as a linear combination of the other two, would it be correct to say v1 = 0(v2)  1(v3)
Question 2
The following matrix is row equivalent to A. Find the general solution to Ax = 0
1  4  2  0  3  5 
0  0  1  0  2  1 
0  0  0  0  0  1 
0  0  0  0  0  0 
I get that the basic variables are x1 and x3, since they are pivots. But is x6 a basic variable or is it free? I'm confused because 1x6 = 0 and 0x6 = 0.

Re: Two quick questions
Question 1: yes
Question 2:
What you end up getting after bringing that matrix on RREF is
,
we see that the free variables are and the lead variables are since they are the pivots.
You ask if are free, it's not because the only value it can take is 0 since it is a pivot in the third row.

Re: Two quick questions
is equivalent to the three equations
From the last, so that and . Putting that into the first equation, . Then the best we can do is say and take , and as parameters, , , , , , .