7. Let T: R³ R2 be the linear transformation defined by T (:))- x - 2y x+y=3z and let B = u₁, U2, U3} and B' = {V₁, V2} be bases for IR³ and R2, respectively, where [1,0,0], u₂ = [0, 1, 0], u3 = [0, 0, 1]; v₁ = [0, 1], V₂ = [1,0]T. U₁ = (a) Find the matrix for T relative to the bases B and B'. (b) Find [T(v)] B if [v]B = [1, 3, -2]T.
7. Let T: R³ R2 be the linear transformation defined by T (:))- x - 2y x+y=3z and let B = u₁, U2, U3} and B' = {V₁, V2} be bases for IR³ and R2, respectively, where [1,0,0], u₂ = [0, 1, 0], u3 = [0, 0, 1]; v₁ = [0, 1], V₂ = [1,0]T. U₁ = (a) Find the matrix for T relative to the bases B and B'. (b) Find [T(v)] B if [v]B = [1, 3, -2]T.
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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![7. Let T: R³ →→ R2 be the linear transformation defined by
(ED) -
T
U₁ =
x - 2y
x+y=3z
and let B = {u₁, U2, U3} and B' = {V₁, V2} be bases for IR³ and R², respectively, where
[1,0,0], u₂ = [0, 1, 0], u3 = [0, 0, 1]; v₁ = [0, 1]T, V₂ = [1,0]T.
V2
(a) Find the matrix for T relative to the bases B and B'.
(b) Find [T(v)] B if [v]B = [1, 3, -2]T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98fdc1e3-416c-49e2-9808-872164c20a53%2F6d0352c7-b86f-4400-97fc-4faa490a788a%2Fmp6wiqr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Let T: R³ →→ R2 be the linear transformation defined by
(ED) -
T
U₁ =
x - 2y
x+y=3z
and let B = {u₁, U2, U3} and B' = {V₁, V2} be bases for IR³ and R², respectively, where
[1,0,0], u₂ = [0, 1, 0], u3 = [0, 0, 1]; v₁ = [0, 1]T, V₂ = [1,0]T.
V2
(a) Find the matrix for T relative to the bases B and B'.
(b) Find [T(v)] B if [v]B = [1, 3, -2]T.
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