1. Problem statement: Find the rank of the matrix below and determine the type of solution of $A\vec{x}=\vec{0}$ for the first matrix given. 2. Matrix to analyze. $$A=\begin{pmatrix}0 & 4 & 0 & -3\\3 & 0 & -4 & -3\\1 & 4 & 3 & 2\\2 & -1 & 0 & -3\end{pmatrix}$$ 3. Formula and rules used. The rank of a matrix is the number of pivot (leading 1) rows in its RREF. For a homogeneous system $A\vec{x}=\vec{0}$ with $n$ unknowns: if $\text{rank}(A)=n$ the system has only the trivial solution; if $\text{rank}(A)