Please help with augenmented matrix of a linear system of equations and is in a Reduced Echelon form

Question

Matrix

is an augenmented matrix of a linear system of equations and is in a Reduced Echelon form.

If the system has only 1 solution, then

A.)a=1, b=0, c can be any value

B.)a=1, b=1, c=0

C.)a=0, b=c=1

D.) a=0, b=1, c=0

Answer 1

Hi Fizaa,

The answer is B.

Cases C and D will result in infinitely many solutions (one free paramter).

Case A is not in reduced row echelon form

Case B is in reduced row echelon from and will result in a unique solution of :

x3=0, X2=2, and x1=1.