Why does this linear system have no solution?

Question

\begin{bmatrix} -7 & 0 & 0 & 0 \\ 0 & 9 & -4 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix}

I believe that this augmented matrix has infinitely many solutions but don't know why the answer says it has no solution.

Answer 1

It has solutions $x=0,y=4t,z=9t.$

Answer 2

If I interpret your question as $Ax=b$, where $b$ is a column vector and you append $A$ and $b$ and reduce it to the augmented matrix above. Then yes, the zero vector is a solution and in fact is has infinitely many solution.