B = -2 {[1] ·[5]} and = {[] [4])} C 3 are bases for R². Complete the augmented matrix used to find the change of coordinates matrix P C←B Ex: 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The image presents a mathematical problem related to linear algebra, specifically the change of coordinates using bases. The given bases \(\mathcal{B}\) and \(\mathcal{C}\) for \(\mathbb{R}^2\) are:

\[
\mathcal{B} = \left\{ \begin{bmatrix} -2 \\ -1 \end{bmatrix}, \begin{bmatrix} -5 \\ 3 \end{bmatrix} \right\}
\]

\[
\mathcal{C} = \left\{ \begin{bmatrix} 1 \\ 6 \end{bmatrix}, \begin{bmatrix} 4 \\ -1 \end{bmatrix} \right\}
\]

The task is to complete the augmented matrix used to find the change of coordinates matrix \( P_{\mathcal{C} \leftarrow \mathcal{B}} \).

The matrix is represented visually with textboxes provided for input:

\[
\begin{bmatrix}
\text{Ex: 0} & & \\
& & \\
& & 
\end{bmatrix}
\]

The aim is to determine the elements of this matrix that would facilitate the change of basis transformation between \(\mathcal{B}\) and \(\mathcal{C}\).
Transcribed Image Text:The image presents a mathematical problem related to linear algebra, specifically the change of coordinates using bases. The given bases \(\mathcal{B}\) and \(\mathcal{C}\) for \(\mathbb{R}^2\) are: \[ \mathcal{B} = \left\{ \begin{bmatrix} -2 \\ -1 \end{bmatrix}, \begin{bmatrix} -5 \\ 3 \end{bmatrix} \right\} \] \[ \mathcal{C} = \left\{ \begin{bmatrix} 1 \\ 6 \end{bmatrix}, \begin{bmatrix} 4 \\ -1 \end{bmatrix} \right\} \] The task is to complete the augmented matrix used to find the change of coordinates matrix \( P_{\mathcal{C} \leftarrow \mathcal{B}} \). The matrix is represented visually with textboxes provided for input: \[ \begin{bmatrix} \text{Ex: 0} & & \\ & & \\ & & \end{bmatrix} \] The aim is to determine the elements of this matrix that would facilitate the change of basis transformation between \(\mathcal{B}\) and \(\mathcal{C}\).
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