Answer
The system Ax =4z is consistent.
Work Step by Step
If the equation Ax = b has a unique solution, then the associated system of equations does not have any free variables. If every variable is a basic variable, then each column of A is a pivot column. So the reduced echelon form of A must be$\left[\begin{array}{ l l l l }1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]$. Now it is clear that A has a pivot position in each row. By Theorem 4, the columns of A span $R^4$.
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