Let F : R3 → R² be defined by F(x,y, z) = (2x + y – z, 3x – 2y + 4z). - (a) Find the matrix A of F relative to the bases B = {(1, 1,1), (1, 1,0), (1, 0,0)} and B' = {(1, 3), (1, 4)}. (b) Verify that, for any v = (a, b, c) in Rº, A[v]B = [F(v)]B'.

Let F : R3 → R² be defined by F(x,y, z) = (2x + y – z, 3x – 2y + 4z). - (a) Find the matrix A of F relative to the bases B = {(1, 1,1), (1, 1,0), (1, 0,0)} and B' = {(1, 3), (1, 4)}. (b) Verify that, for any v = (a, b, c) in Rº, A[v]B = [F(v)]B'.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let F : R3 → R² be defined by F(x,y, z) = (2x + y – z, 3x – 2y + 42).
(a) Find the matrix A of F relative to the bases
B = {(1, 1,1), (1,1,0), (1, 0, 0)} and B' = {(1,3), (1,4)}.
(b) Verify that, for any v =
(a,b, c) in R³, A[v)B = [F(v)]B'.

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