Solution: With T defined by T(x)=A x, find a vector x whose image under T is b, and determine whether \boldsymbolx is unique.



Question: With \(T\) defined by \(T(x)=A x\), find a vector \(x\) whose image under \(T\) is \(b\), and determine whether \(\boldsymbol{x}\) is unique.

\[A=\left[\begin{array}{ccc} 1 & 0 & -3 \\ -3 & 1 & 6 \\ 2 & -2 & -1 \end{array}\right], \quad b=\left[\begin{array}{c} -2 \\ 3 \\ -1 \end{array}\right]\]

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