Given the system whose augmented matrix is
1 1 1 1
1 −1 0 a
0 1 b 0
Determine (if possible) conditions on a and b such that this system has (a) no solution (b) many solutions (c) a unique solution.
-No solution: row of zero
-Many solutions: one or more free variables
-Unique solution: pivot in every column
The Attempt at a Solution
I tried to do it, but my answers were wrong. The good answers are a) b=1/2, a≠1 b) b=1/2, a=1 c) b≠1/2.
I tried to reduce the matrix and I had:
0 0 1-2b 1-3a
1 0 b 2a
0 1 b a
Can someone explain how to reduce the matrix properly or what am I doing wrong?