Let's take an example of system of equations(actually they are all same)
It is homogeneous system of linear equations. Therefore it has zero solution [0,0,0].
Rank of those coefficient matrix is found to be 1.
I read in textbook that it will have (n-r) linearly independent solutions where n= number of variables & r= rank of coefficient matrix.
So for above example it'll have (3-1)=2 linearly independent solutions.
I'll list some solutions out of infinitely many solutions:
[-2, 1,0] & so on.
1)where are the 2 linearly independent solutions?
2)out of many solutions, 2 are found to be linearly independent. Is the rest of solutions Linearly dependent solutions?
3) what is actually meant by linearly dependence / independence?