I have a matrix A,
This matrix is equal to the following, where ^T = transpose
A= [u1 u2 u3] u1 = (1, 1, 1, 3)^T u2 = (1, 0, 2, 2)^T u3 = (1, −4, 1, 4)^T
I'm looking to determine whether or not the columns of A are linearly independent in R4
Here is where I'm uncertain, with the transpose of the vectors, this is the resulting matrix
1 1 1 1 0 -4 1 2 1 3 2 4
If i'm looking for the values of each, c1,c2,c3,c4, are these values now based on the rows because of the transposition?
1c1 1c1 1c1 1c2 0c2 -4c2 1c3 2c3 1c3 3c4 2c4 4c4
Or does it stay normalized?
1c1 1c2 1c3 1c1 0c2 -4c3 1c1 2c2 1c3 3c1 2c2 4c3
I realize that this may be an odd question, but the math department at my school hires grad students and adjuncts to instruct class.