5. Let T: R3 >R³ be a linear operator and B= {V1, V2, V3} a basis for R3. Suppose[0]T(v1) :,T(v2)5,T(v3)2121a. Determine whether w =| 1 is in range of T.2b. Find a basis for R(T).c. Find dim(N(T))

Given: T:R3→R3 be a linear operator and B=v1,v2,v3 a basis for R3.Tv1=-121,Tv2=050,Tv3=-1-12

Let T: R3 >R³ be a linear operator and B = {V1, V2, V3} a basis for R³. Suppose [0] -1 T(v,) 2 ,T(v2) 5,T(v3) -1 Lo. 2 -21 a. Determine whether w = 1 is in range of T. b. Find a basis for R(T). c. Find dim(N(T)) 5.

Let T: R3 >R³ be a linear operator and B = {V1, V2, V3} a basis for R³. Suppose [0] -1 T(v,) 2 ,T(v2) 5,T(v3) -1 Lo. 2 -21 a. Determine whether w = 1 is in range of T. b. Find a basis for R(T). c. Find dim(N(T)) 5.

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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5. Let T: R3 >R³ be a linear operator and B
= {V1, V2, V3} a basis for R3. Suppose
[0]
T(v1) :
,T(v2)
5,T(v3)
2
1
21
a. Determine whether w =| 1 is in range of T.
2
b. Find a basis for R(T).
c. Find dim(N(T))

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