The following matrix is a reduced augmented matrix obtained from a system of equations.

Question

1 0 1 3

0 1 4 -2

0 0 0 0

The number of solutions to the system is

a.)none

b.) one

c)infinite

Answer 1

From the given matrix, corresponds to the system is

x + z = 3

y + 4z = -2

0 = 0

Letting z=t, we find that y=−2 -4t  and x =3−t.

Thus, the system has infinitely many solutions, parametrized for all t.

So option C is correct.