Let A = \left[\begin{array}{ccc}
2 &2 &5\cr
3 &4 &4\cr
5 &3 &-4\cr
31 &32 &27
\end{array}\right] \ \mbox{ and } \ \vec{b} = \left[\begin{array}{c}
13\cr
17\cr
14\cr
152
\end{array}\right].
Define the linear transformation T: {\mathbb R}^3 \rightarrow {\mathbb R}^4 by T(\vec{x}) = A\vec{x} .
Find a vector \vec{x} whose image under T is \vec{b} .

\vec{x} = \left[\Rule{0pt}{3.6em}{0pt}\right. \left]\Rule{0pt}{3.6em}{0pt}\right. .

Is the vector\vec{x} unique?
choose
unique
not unique

Is the vector

In order to get credit for this problem all answers must be correct.