Determine the Number of Solutions to the Augmented Matrix $\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$

Multiple Choice

Determine the number of solutions to the augmented matrix.
$\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$

A) infinitely many
B) 2 solutions
C) 1 solution
D) no solutions