Reeves Hammond
06/26/2023 · Elementary School
2. Let \( \left.A=\left[\begin{array}{cc}1 & -3 \\ 3 & 5 \\ -1 & 7\end{array}\right], \vec{u}=\left\lvert\, \begin{array}{c}2 \\ -1\end{array}\right.\right], \vec{b}=\left|\begin{array}{c}3 \\ 2 \\ -5\end{array}\right|, \vec{c}=\left|\begin{array}{l}3 \\ 2 \\ 5\end{array}\right| \) and defined transformation \( T: R^{2} \rightarrow R^{3} \) by \( T(\vec{x})=A(\vec{x}) \). a. Find \( T(\vec{u}) \). b. Find an \( \vec{x} \) in \( R^{2} \) whose image under \( T \) is \( \vec{b} \) c. Is more than one \( \vec{x} \) whose image under \( T \) is \( \vec{b} \) ? d. Determine if \( \vec{c} \) is in the range of the transformation \( T \)
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a. \( T(\vec{u}) = \begin{bmatrix} 5 \\ 1 \\ -9 \end{bmatrix} \)
b. \( \vec{x} = \begin{bmatrix} \frac{3}{2} \\ -\frac{1}{2} \end{bmatrix} \)
c. Yes, there are infinitely many solutions for \( T(\vec{x}) = \vec{b} \).
d. \( \vec{c} \) is not in the range of the transformation \( T \).
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