### Example 1**Problem:**Find the matrix \( A' \) for \( T \) relative to the basis \( B' \).- **Transformation:** \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \), defined as \( T(x, y) = (x - y, y - 2x) \).- **Basis \( B' \):** \(\{(1, -2), (0, 3)\}\)**Attempted Solution:**\[ A' = \begin{bmatrix} 3 & -3 \\ 11/3 & -4 \end{bmatrix} \]- The result here is marked with a red cross, indicating the matrix \( A' \) is incorrect.### Example 2**Problem:**Find the matrix \( A' \) for \( T \) relative to the basis \( B' \).- **Transformation:** \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \), defined as \( T(x, y) = (-7x + y, 7x - y) \).- **Basis \( B' \):** \(\{(1, -1), (-1, 5)\}\)**Attempted Solution:**\[ A' = \begin{bmatrix} 48 & -72 \\ -16 & 24 \end{bmatrix} \]- The result here is marked with a red cross, indicating the matrix \( A' \) is incorrect.### NotesIn both examples, the transformation and the basis for the transformation are given, but errors are identified in the attempted matrix calculations. Each solution attempt results in an incorrect matrix, as indicated by the red crosses.

Answered: Find the matrix A' for T relative to…

Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x - y, y - 2x), B' = {(1, -2), (0, 3)} 3 11/3 -3 -4

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Similar questions

Find the matrix A' for T relative to the basis B'. A': = T: R² → R², T(x, y) = (−6x + y, 6x − y), B' = {(1, −1), (-1,5)} -
9. Let and B 3 = {[B]-[-2]} = B' ={[2¹].[6]} be two ordered bases for R². Find the change of basis matrix [I]B'.
Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1), (1, -1)} A' =
Let B={(1, 0), (0, 1)} and B'= {(1, 2), (2, 3)} be any two bases of R². Then verify PT],P= [T], where T(x, y)=(2x-3y, x +y) and P is the B'> transition matrix from B to B'.
Find the coordinate matrix of x in R" relative to the basis B. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)), x = (-4, 19, -8) [x] = 000 11 It 7
Find the transition matrix from the basis B = {(1,2,3) (1,0,1)(1,2,1)} to B' = {(1,1,0)(0,1,1)(1,1,1)}.