4) Let T : R3 → R3 be a linear operator and B = {v1 v2 v3} a basisfor R3 such that T(v, ) = (-1,2,1),T(v2 ) = (0,5,0) and%3D%3DT (v3) = (-1,-1,2)a) Determine whether w = (-2,1,2)is in the range of Tb) Find the kernel of T

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{v1.v2,V3} a basis for R³ such that T(v2 ) = (-1,2,1),T(v2 ) = (0,5,0) and 4) Let T : R3 → R3 be a linear operator and B = T (v3) = (-1,–1,2) a) Determine whether w = (-2,1,2)is in the range of T b) Find the kernel of T

{v1.v2,V3} a basis for R³ such that T(v2 ) = (-1,2,1),T(v2 ) = (0,5,0) and 4) Let T : R3 → R3 be a linear operator and B = T (v3) = (-1,–1,2) a) Determine whether w = (-2,1,2)is in the range of T b) Find the kernel of 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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Question

4) Let T : R3 → R3 be a linear operator and B = {v1 v2 v3} a basis
for R3 such that T(v, ) = (-1,2,1),T(v2 ) = (0,5,0) and
%3D
%3D
T (v3) = (-1,-1,2)
a) Determine whether w = (-2,1,2)is in the range of T
b) Find the kernel of T

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