- #1
Dustinsfl
- 2,281
- 5
Determine the spanning set of {(1,0,0)^T, (0,1,1)^T, (1,0,1)^T, (1,2,3)^T}
v=a*(1,0,0)^T+b*(0,1,1)^T+c*(1,0,1)^T+d*(1,2,3)^T
Augmented Matrix(3, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 1, (1, 4) = 1, (1, 5) = v1, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 2, (2, 5) = v2, (3, 1) = 0, (3, 2) = 1, (3, 3) = 1, (3, 4) = 3, (3, 5) = v3})
In reduced row echelon, Matrix(3, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = v1-v3+v2, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 2, (2, 5) = v2, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 1, (3, 5) = v3-v2})
I am not sure how to finish this off since there is an extra column.
v=a*(1,0,0)^T+b*(0,1,1)^T+c*(1,0,1)^T+d*(1,2,3)^T
Augmented Matrix(3, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 1, (1, 4) = 1, (1, 5) = v1, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 2, (2, 5) = v2, (3, 1) = 0, (3, 2) = 1, (3, 3) = 1, (3, 4) = 3, (3, 5) = v3})
In reduced row echelon, Matrix(3, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = v1-v3+v2, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 2, (2, 5) = v2, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 1, (3, 5) = v3-v2})
I am not sure how to finish this off since there is an extra column.