Find all values a for which is in the span of . Also find the values of a for which are linearly independent.
When I try to do rref I get all zeros in the bottom...
For the first problem you want all a such that x[1 a a]+ y[a 1 a]+ z[a a 1]= [1 1 1] for some numbers x, y, z. That gives the three equations x+ ay+az= 1, ax+y+az= 1, and ax+ay+ z= 1. For what values of a does that have a solution?
For the second problem you want to look at x[1 a a]+ y[a 1 a]+ z[a a 1]= [0 0 0]. An obvious solution is x=y= z= 0. For what values of a is that the only solution?
Are you saying you get all zeros in the last row of the augmented matrix, for all a?