Let T: R3 →R³ be a linear operator and B = {V1, V2, V3} a basis for R3. Suppose [0] %3D T(v;) = 2 ,T(v2) |.T(v,) = 5 .T(v2) %3D Lo] 2 -2] a. Determine whether w = | 1 1 is in range of T. 2 b. Find a basis for R(T). C Find dim(N(T))

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I dont know how to answer this question, it would be very helpful, if you could ans this question with a clear explanation for my understanding.

{v1,V2, V3} a basis for R3. Suppose
[0]
= |5|,T(v3) =
Lol
5.
Let T: R3 →R3 be a linear operator and B =
%3D
-E
[-1]
T(v,) =
2 ,T(v2)
-2]
1 is in range of T.
a. Determine whether w =
b. Find a basis for R(T).
c. Find dim(N(T))
Transcribed Image Text:{v1,V2, V3} a basis for R3. Suppose [0] = |5|,T(v3) = Lol 5. Let T: R3 →R3 be a linear operator and B = %3D -E [-1] T(v,) = 2 ,T(v2) -2] 1 is in range of T. a. Determine whether w = b. Find a basis for R(T). c. Find dim(N(T))
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