Augenmented matrix...Please help!!!

Question

The following augenmented matrix of a linear system of equations is in a Reduced Echelon form.

Answer 1

a) If b = 0 and c = 0, there are infinitely many solutions for all values of a.

The first and second row together define a line. With no restrictions in line c, then, we have a line of solutions.

b) If b is not equal to 0, there is one solution. The determinant of the matrix is b not equal to 0, which means that the matrix is invertible, implying one solution.

c) If b = 0 and c is not equal to 0, there is no solution. Labeling the variables x, y, z, we have 0z = b, which has no solution if b is not equal to 0.