b) Let T:R³ R³ be a linear transformation, and let B = {e₁, e2, e3} be the standard basisfor R³.Suppose that,[2][1]T(e₁) = 1[ ]T(e3) =L2.-31i) Find T(v), where v= 21[5ii) Is w6 in R(T)?-6]T(e₂) = 32

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Answered: b) Let T:R³ R³ be a 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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1. Let T : R² → R³ be a linear transformation such that T(e1) = u1 and T(e2) = u2, where e1, e2 8 is the standard unit vectors of R² and u1 3 and u2 = 2. Then find T 1 -2 6.
Suppose T: R2-→R³ is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(-3U-2V). 14 18 U = V = T(U) = -7 T(V) =-9 3 16 21 T(-3U–2V) = | 0
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b) Let T:R³ R³ be a linear transformation, and let B = {e₁, e2, e3} be the standard basis for R³. Suppose that, [1] T(e) = 1, [3]. [2] T(e3) = 2 L2. -31 i) Find T(v), where v= 2 1 [5 ii) Is w6 in R(T)? -61 T(e₂) = 3