The discussion revolves around finding the dimension of the linear span of three given vectors in a vector space context.
There is an ongoing examination of the row reduction results, with some participants affirming the findings while others express doubt about the independence of the vectors. Multiple interpretations of the results are being explored, particularly regarding the dimension of the span.
Participants are working under the assumption that the vectors are in a three-dimensional space and are checking for linear independence through matrix row reduction.
HallsofIvy said:Yes, it does. What you have shown is that those three vectors are independent and independent vectors form a basis for their span.
Dick said:It would mean that. Except I think you did the row reduction wrong. Those vectors aren't linearly independent.
lolimcool said:oops i did i did it again and got
1 0 5
0 1 -3
0 0 0
so dimension = 2?