Consider the following linear transformation and basis. Find the standard matrix A for the linear transformation. A = Find the transition matrix P from B' to the standard basis B and then find its inverse. P = p-1 T: R² R², T(x, y) = (x - 5y, y - x), B' = {(1, -2), (0, 3)} = A' = ↓ ↑ Find the matrix A' for T relative to the basis B'. 11 ↓ 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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Consider the following linear transformation and basis.
Find the standard matrix A for the linear transformation.
A =
Find the transition matrix P from B' to the standard basis B and then find its inverse.
P =
T: R² R², T(x, y) = (x - 5y, yx), B' = {(1, -2), (0, 3))
p-1 =
A' =
↓1
↓ 1
Find the matrix A' for T relative to the basis B'.
Transcribed Image Text:Consider the following linear transformation and basis. Find the standard matrix A for the linear transformation. A = Find the transition matrix P from B' to the standard basis B and then find its inverse. P = T: R² R², T(x, y) = (x - 5y, yx), B' = {(1, -2), (0, 3)) p-1 = A' = ↓1 ↓ 1 Find the matrix A' for T relative to the basis B'.
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