Please answer only the blank ones The image presents a sequence of steps to find matrices related to a transformation T from R² to R² with respect to two different bases, B and B'.**Problem Statement and Given Data:**- Let \( B = \{(1, 3), (-2, -2)\} \) and \( B' = \{(-12, 0), (-4, 4)\} \) be bases for \( R^2 \).- Let \( A = \begin{bmatrix} 2 & 0 \\ 4 & 3 \end{bmatrix} \) be the matrix for transformation \( T: R^2 \to R^2 \) relative to basis B.**Tasks and Solutions:**(a) **Find the Transition Matrix \( P \) from \( B' \) to B:**- Transition Matrix \( P \) is given as: \[ P = \begin{bmatrix} 6 & 4 \\ 9 & 4 \end{bmatrix} \](b) **Use the Matrices \( P \) and \( A \) to Find \([v]_B\) and \([Tv]_B\):**- Given \([v]_B = \begin{bmatrix} -2 \\ 1 \end{bmatrix}^T\)- Calculate \([v]_{B'}\): \[ [v]_{B'} = \begin{bmatrix} -8 \\ -14 \end{bmatrix} \]- Error in calculating \([Tv]_{B'}\): \[ [Tv]_{B'} = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \] (Boxes indicate missing values)(c) **Find \( P^{-1} \) and \( A' \) (the Matrix for \( T \) Relative to \( B' \)):**- Inverse of Transition Matrix \( P \): \[ P^{-1} = \begin{bmatrix} -1/3 & 1/3 \\ 3/4 & 1/2 \end{bmatrix} \]- Matrix \( A' \): \[ A' = \begin{bmatrix} 13 & 20/3 \\ -33/2 & -8 \end{bmatrix}

Name: Please answer only the blank ones The image presents a sequence of ste
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please answer only the blank ones The image presents a sequence of steps to find matrices related to a transformation T from R² to R² with respect to two different bases, B and B'.**Problem Statement and Given Data:**- Let \( B = \{(1, 3), (-2, -2)\}