\begin{bmatrix} 1& 1& 1& 0& 0\\ 0& 1& 1& 0& 0\\ 0& 0& 1& -1& 1 \end{bmatrix}
This problem is related to Linear Optimization where this matrix is labelled as Coefficient Matrix A and I am expected to find all the basic solutions to this Matrix A. 5 Variables and 3 equality constraints, so there will be 2 Non - Basic Variables and 3 Basic Variables. I do know that we need only Linearly independent columns in order to form bases as part of the basic solutions, but I don't know how you would easily group all the linearly independent columns together.
Like the solution to this problem says that Columns 1, 4, and 5 are linearly dependent and any 3 of the last 4 columns are also linearly dependent, so you would not form bases from them.
But is there some shortcut or trick that can be applied to quickly determine which of the column vectors are dependent so that I can take them out while solving this type of problem?
You mean just slog it through and check all cases..?
– llllllllllllllllllllllllllllll Oct 03 '15 at 03:08