The transformation T:V → V , defined by x +3y —х — 2у — 32 -y+3 Ty a) Determine whether the linear Transformation T is one to one. b) Evaluate the Nullity Space N(T). c) State the dimensional theorem, and then verify it. d) Evaluate the inverse Linear Transformation T-1 and then find the vector T-1 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The subject is Linear Algebra ( Constructing Linear Transformations and

Diagonalization of Linear Operators )

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The transformation
T:V → V , defined by
х + Зу
—х — 2у — 3z
T
||
-у + 3z
a) Determine whether the linear Transformation T is one to one.
b) Evaluate the Nullity Space N(T).
c) State the dimensional theorem, and then verify it.
d) Evaluate the inverse Linear Transformation T
y
and then find the
vector T-
2
3.
Transcribed Image Text:The transformation T:V → V , defined by х + Зу —х — 2у — 3z T || -у + 3z a) Determine whether the linear Transformation T is one to one. b) Evaluate the Nullity Space N(T). c) State the dimensional theorem, and then verify it. d) Evaluate the inverse Linear Transformation T y and then find the vector T- 2 3.
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