Given: L: R³ R³, L(x, y, z) = (x+2y-z, -y,x+7z), ordered bases B = {(1, 0, 0), (0, 1,0), (0, 0, 1)}, B = {(1, 0, 0), (1, 1,0), (1, 1, 1)} a. Find the matrix representation of L wrt B. b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B' c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
Given: L: R³ R³, L(x, y, z) = (x+2y-z, -y,x+7z), ordered bases B = {(1, 0, 0), (0, 1,0), (0, 0, 1)}, B = {(1, 0, 0), (1, 1,0), (1, 1, 1)} a. Find the matrix representation of L wrt B. b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B' c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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![- Given: L: R³ R³, L(x, y, z) = (x+2y-z,-y,x+7z),
ordered bases B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}, B' = {(1, 0, 0), (1, 1,0), (1, 1, 1)}
a. Find the matrix representation of L wrt B.
b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B'
c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215eb24e-0d44-4675-8884-3702528e58cf%2F8cdc2a6f-a05d-499e-a305-ffb5199f87d9%2Fkac9dpi_processed.png&w=3840&q=75)
Transcribed Image Text:- Given: L: R³ R³, L(x, y, z) = (x+2y-z,-y,x+7z),
ordered bases B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}, B' = {(1, 0, 0), (1, 1,0), (1, 1, 1)}
a. Find the matrix representation of L wrt B.
b. Find the change of basis matrix: (i.) from B' to B; (ii.) from B to B'
c. Determine the matrix rep. of L wrt B' using the matrices in (a) and (b).
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