7. Let T: R² R2 be the linear transformation defined by T(x, y) = (2x +2y, x+3y) relative to the basis S = {u₁ = (1, 1), u₂ = (1, 0)} of R².a. Find T(u₁).b. Write T(₁) as a linear combination of u₁ and u₂.c. Find T(u₂).d. Write T(u2) as a linear combination of u₁ and u2.e. Find [T]s, the matrix representation of T relative to S.

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Answered: 7. Let T: R² → R² be the linear…

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: R² → R² be the linear transformation defined by T(x, y) = (2x + 2y, z + 3y) relative to the basis S = {u₁ = (1, 1), u₂ = (1,0)} of R². a. Find T(₁). b. Write T(₁) as a linear combination of u₁ and u₂. c. Find T(u₂).