Consider the following linear transformation. T: P₂ → R³ defined by T(a + bx + cx²) Find the nullity of T. nullity(7) = Determine if the linear transformation is one-to-one. one-to-one not one-to-one = 4a - b a + b - 5c c-a Determine if the linear transformation is onto. Onto, because T is not one-to-one and the kernel is trivial. Onto, because T is one-to-one and the domain and codomain have the same dimension. Not onto, because T one-to-one and the kernel is nontrivial. Not onto, because T is not one-to-one and the domain and codomain have the same dimension.
Consider the following linear transformation. T: P₂ → R³ defined by T(a + bx + cx²) Find the nullity of T. nullity(7) = Determine if the linear transformation is one-to-one. one-to-one not one-to-one = 4a - b a + b - 5c c-a Determine if the linear transformation is onto. Onto, because T is not one-to-one and the kernel is trivial. Onto, because T is one-to-one and the domain and codomain have the same dimension. Not onto, because T one-to-one and the kernel is nontrivial. Not onto, because T is not one-to-one and the domain and codomain have the same dimension.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 76E: A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h...
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![Consider the following linear transformation.
T: P2
Find the nullity of T.
nullity (7) =
R³ defined by T(a + bx + cx²) =
Determine if the linear transformation is one-to-one.
O one-to-one
O not one-to-one
Determine if the linear transformation is onto.
4a - b
a + b 5c
[***]
c-a
Onto, because T is not one-to-one and the kernel is trivial.
O Onto, because T is one-to-one and the domain and codomain have the same dimension.
Not onto, because T one-to-one and the kernel is nontrivial.
O Not onto, because T is not one-to-one and the domain and codomain have the same dimension.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9803fb3b-dfc9-4d82-9841-2445951838a9%2F58ea7cee-78b8-4d25-9f61-32c41221a486%2F18p9yrf_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following linear transformation.
T: P2
Find the nullity of T.
nullity (7) =
R³ defined by T(a + bx + cx²) =
Determine if the linear transformation is one-to-one.
O one-to-one
O not one-to-one
Determine if the linear transformation is onto.
4a - b
a + b 5c
[***]
c-a
Onto, because T is not one-to-one and the kernel is trivial.
O Onto, because T is one-to-one and the domain and codomain have the same dimension.
Not onto, because T one-to-one and the kernel is nontrivial.
O Not onto, because T is not one-to-one and the domain and codomain have the same dimension.
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