Question

Jump to level 1 \begin{align} \text{Let } T: \mathbb{R}^3 \to \mathbb{R}^2 \text{ be defined by } T \begin{bmatrix} x_1\\x_2\\x_3 \end{bmatrix} = \begin{bmatrix} 3x_1 - x_2\\-3x_3 \end{bmatrix} . \\ \text{Let } B = \left\{ \mathbf{u}_1 = \begin{bmatrix} -6\\-5\\-7 \end{bmatrix}, \mathbf{u}_2 = \begin{bmatrix} 0\\3\\-4 \end{bmatrix}, \mathbf{u}_3 = \begin{bmatrix} 5\\-1\\2 \end{bmatrix} \right\} \text{ and } C = \left\{ \mathbf{v}_1 = \begin{bmatrix} 5\\6 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 7\\-2 \end{bmatrix} \right\} . \\ \text{What augmented matrix should be used to find } [T]_B^C, \text{ the matrix representation of } T \text{ with respect to the bases } B \text{ and } C. \begin{bmatrix} \text{Ex: } 5 & & &\\ & & & \end{bmatrix} \end{align}

          Jump to level 1
\begin{align*}
\text{Let } T: \mathbb{R}^3 \to \mathbb{R}^2 \text{ be defined by } T \begin{bmatrix} x_1\\x_2\\x_3 \end{bmatrix} = \begin{bmatrix} 3x_1 - x_2\\-3x_3 \end{bmatrix} .
\\ \text{Let } B = \left\{ \mathbf{u}_1 = \begin{bmatrix} -6\\-5\\-7 \end{bmatrix}, \mathbf{u}_2 = \begin{bmatrix} 0\\3\\-4 \end{bmatrix}, \mathbf{u}_3 = \begin{bmatrix} 5\\-1\\2 \end{bmatrix} \right\} \text{ and } C = \left\{ \mathbf{v}_1 = \begin{bmatrix} 5\\6 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 7\\-2 \end{bmatrix} \right\} .
\\ \text{What augmented matrix should be used to find } [T]_B^C, \text{ the matrix representation of } T \text{ with respect to the bases } B \text{ and } C.
\begin{bmatrix} \text{Ex: } 5 & & &\\ & & & \end{bmatrix}
\end{align*}

$Jump to level 1 Let T: ℝ^3 →ℝ^2 be defined by T = . Let B = {𝐮1 = , 𝐮2 = , 𝐮3 = } and C = {𝐯1 = , 𝐯2 = } . What augmented matrix should be used to find [T]B^C, the matrix representation of T with respect to the bases B and C. $

Added by Jeffrey C.

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