Please help me with this question.

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

From the 3rd row, a = 0, which eliminates choices A and B.

From the second row, b + c = 2 So, choice C is the only one that makes sense.

Answer 2

HI Fizaa,

The answer is B.

Cases C and D will result in infinitely many solutions, since each will result in a free paramter.

Case A will not be in reduced row echelon form.

Case B will result in x3=0, x2=2, and x1=1.