- #1
JonathanT
- 18
- 0
Ok so I just got my test back for Linear Algebra and I was told to find a basis for the ker(A) where A = \begin{array}{cccc} 1 & 1 & 0 & 1 \\ 1 & 0 & -1 & 0 \\ 0 & 1 & 1 & 1 \\ -1 & 1 & -1 & -2 \end{array}
now I computed Ax = 0 and found x = [-t, 0 ,-t, t]^T. where x4 = t.
Then I wrote the basis as [1,0,1,-1]^T because I was under the impression that the basis is unique to any scalar multiple of the basis. So I simply took the scalar -1 to make as much of the basis positive as possible as I understand the convention is.
Am I wrong is thinking that the basis for the Ker(A) is [1,0,1,-1]^T as well as [-1,0,-1,1]^T?
I was marked of 6 points for this problem and I just wanted to make sure my logic was correct before I took a trip to the TA and looked like an idiot.
Thanks for your time.
now I computed Ax = 0 and found x = [-t, 0 ,-t, t]^T. where x4 = t.
Then I wrote the basis as [1,0,1,-1]^T because I was under the impression that the basis is unique to any scalar multiple of the basis. So I simply took the scalar -1 to make as much of the basis positive as possible as I understand the convention is.
Am I wrong is thinking that the basis for the Ker(A) is [1,0,1,-1]^T as well as [-1,0,-1,1]^T?
I was marked of 6 points for this problem and I just wanted to make sure my logic was correct before I took a trip to the TA and looked like an idiot.
Thanks for your time.
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