This is the question I am working on : identify a largest subcollection of linearly independent vectors and express all the remaining vectors as linear combinations of the vectors in the subcollection. (a) [4 points] $v_1 = (5, 2, −3, 1)$, $v_2 = (4, 1, −2, 3)$, $v_3 = (1, 1, −1, −2)$, $v_4 = (3, 4, −1, 2)$, $v_5 = (7, −6, −7, 0)$;
The method I found from one of the stack exchange posts :
- Put vectors as COLUMNS in a matrix
- Find RREF
- Identify non-pivotal columns in RREF matrix and then the corresponding columns in the original matrix are the linearly independent ones.
But I tried to do this by : 1.Putting vectors as ROWS in a matrix 2.Find RREF 3.Identify non-pivotal rows in RREF and then the corresponding rows in the original matrix are the linearly independent ones.
But I'm getting a wrong set here. What Am I doing wrong? : While doing the RREF, I did permute rows, I am assuming that is the problem here. However, then I should have done Reduced Column Echelon Form right? But I have read that RREF = (RCEF)transpose.
Thoughts: RREF=RCEF transpose works only for the same matrix so if I put vectors as columns, I should do RREF and if as rows then RCEF. Am I right?