Question Solved1 Answer If \( T \) is defined by \( T(x)=A x \), find a vector \( x \) whose image under \( T \) is \( b \), and determine whether \( x \) is unique. Let \( A=\left[\begin{array}{rrr}1 & -4 & 3 \\ 0 & 1 & -3 \\ 3 & -13 & 9\end{array}\right] \) and \[ \mathbf{b}=\left[\begin{array}{r} -6 \\ -11 \\ -4 \end{array}\right] \] Find a single vector \( x \) whose image If \( T \) is defined by \( T(x)=A x \), find a vector \( x \) whose image under \( T \) is \( b \), and determine whether \( x \) is unique. Let \( A=\left[\begin{array}{rrr}1 & -4 & 3 \\ 0 & 1 & -3 \\ 3 & -13 & 9\end{array}\right] \) and \[ \mathbf{b}=\left[\begin{array}{r} -6 \\ -11 \\ -4 \end{array}\right] \] Find a single vector \( x \) whose image under \( T \) is \( b \). \[ x= \]

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Transcribed Image Text: If \( T \) is defined by \( T(x)=A x \), find a vector \( x \) whose image under \( T \) is \( b \), and determine whether \( x \) is unique. Let \( A=\left[\begin{array}{rrr}1 & -4 & 3 \\ 0 & 1 & -3 \\ 3 & -13 & 9\end{array}\right] \) and \[ \mathbf{b}=\left[\begin{array}{r} -6 \\ -11 \\ -4 \end{array}\right] \] Find a single vector \( x \) whose image under \( T \) is \( b \). \[ x= \]
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Transcribed Image Text: If \( T \) is defined by \( T(x)=A x \), find a vector \( x \) whose image under \( T \) is \( b \), and determine whether \( x \) is unique. Let \( A=\left[\begin{array}{rrr}1 & -4 & 3 \\ 0 & 1 & -3 \\ 3 & -13 & 9\end{array}\right] \) and \[ \mathbf{b}=\left[\begin{array}{r} -6 \\ -11 \\ -4 \end{array}\right] \] Find a single vector \( x \) whose image under \( T \) is \( b \). \[ x= \]
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Solution:-A=[[1,-4,3],[0,1,-3],[3,-13,9]],b=[[-6],[-11],[-4]]Now Augumented matrix. using Gauss-Jordan Elimination Method,{:[[[1,-4,3,-6],[0,1,-3,-11],[3,-13,9,-4]]],[R_(3)rarrR_(3)-3R_(1)quad[[1,-4,3,-6],[0,1,-3,-11],[0,-1,0,14]]],[longrightarrow^(R_(1)rarrR_(1)+4R_(2))_(R_(3)rar ... See the full answer