5. Let T: R3 →R³ be a linear operator and B = {V1, V2, V3} a basis for R3. Suppose -1] T(v1) = 2 ,T(v2) 5,T(v3) -21 a. Determine whether w =| 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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5. Let T: R3 →R³ be a linear operator and B =
{V1, V2, V3} a basis for R3. Suppose
T(v1)
2 ,T(v2) =
,T(v3) =
a. Determine whether w =
is in range of T.
2
b. Find a basis for R(T).
c. Find dim(N(T)).
6. T: R? →R² is a linear operator with Band B' ordered bases for v.
x + z
-(ED-
T
= [2y – x
y +z
В —
1
B' =
-11}, v =
3
a. Find the basis representation for T relative to the ordered bases B and B'.
b. Find T(v) using a direct computation and using the matrix representation.
Transcribed Image Text:5. Let T: R3 →R³ be a linear operator and B = {V1, V2, V3} a basis for R3. Suppose T(v1) 2 ,T(v2) = ,T(v3) = a. Determine whether w = is in range of T. 2 b. Find a basis for R(T). c. Find dim(N(T)). 6. T: R? →R² is a linear operator with Band B' ordered bases for v. x + z -(ED- T = [2y – x y +z В — 1 B' = -11}, v = 3 a. Find the basis representation for T relative to the ordered bases B and B'. b. Find T(v) using a direct computation and using the matrix representation.
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