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## Homework Statement

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.

## Homework Equations

-Row reduction

-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?