\[\begin{matrix} x& -&3y&+&z&=&2\\ -3x & -&4y&+&z&= &0\\ & &2y&-&z&=&1 \end{matrix}\]
Let \(A\) be the coefficient matrix corresponding to this system, and let \(\vec {b}=\begin{bmatrix}2\\0\\1\end{bmatrix}\).
Suppose that we find that \((1, -2, -5)\) is a unique solution to this system. What does this tell us? Select ALL that apply.
\(A\) is invertable. Vector \(\vec {b}\) is in the span of the columns of \(A\). Columns of \(A\) are linearly dependent. Equation \(A\vec {x}=\vec {b}\) has a unique
solution. Vector \(\vec {b}\) can be written as a linear combination of the columns of \(A\). \(A\vec {b}=\begin{bmatrix}1\\-2\\-5\end{bmatrix}\)