How to find the number of solutions of an augmented matrix? Given a system of linear equations is represented as a augmented matrix:
$$M = \left[\begin{array}{cccc|c}1&0&8&0&1\\0&1&1&0&3\\0&0&0&1&1\end{array}\right]$$
How do I find the exact number of solutions in the system of equations?
If I'm not mistaken, it has unique solutions, therefore, it shouldn't be inconsistent or have an infinite amount of solutions.
Is it wrong to say that there are 3 solutions?

In case you mean to solve the under-determined system $AX=B:$
$$\begin{pmatrix} 1 & 0 & 8 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1\end{pmatrix}
\begin{pmatrix} w \\x \\ y \\ z \\ \end{pmatrix}= \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix}.$$ Multiply from let with $A^T$ to get
$$\begin{pmatrix} 1 & 0 & 8 & 0\\ 0 & 1 & 1 &0\\ 8 & 1 & 65 & 0 \\ 0 & 0 & 0& 1 \end{pmatrix} \begin{pmatrix} w \\x \\ y \\ z \\ \end{pmatrix}=\begin{pmatrix} 1 \\ 3 \\ 0 \\ 1 \end{pmatrix}. $$
This simple equation can be solved to give $w=1, x=3, y=0, z=1$.
