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
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
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
The subject is Linear Algebra ( Constructing Linear Transformations and
Diagonalization of Linear Operators)
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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.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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