Hi, I need help with this Linear Algebra exercise, please. Thank you!Drop down menu options:T___ontoIs definitely notMight beDefinitely is T is _____one-to-oneIs definitely notMight beDefinitely is nullity(T)Is at most 1At least 1Must equal 1 Suppose that T : R* → R³ is a linear transformation and that T(1, 1, 1,1) = (0,0,0). Choose the optionthat correctly completes each of the following statements.• T [ Select ]onto.• T ( Select ]one-to-one.nullity(T) [Select ]

Name: Hi, I need help with this Linear Algebra exercise, please. Thank you!D
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Description: Hi, I need help with this Linear Algebra exercise, please. Thank you!Drop down menu options:T___ontoIs definitely notMight beDefinitely is T is _____one-to-oneIs definitely notMight beDefinitely is nullity(T)Is at most 1At least 1Must equal 1 Suppose

Answered: Suppose that T : Rª → R³ is a linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Hi, I need help with this Linear Algebra exercise, please. Thank you!

Drop down menu options:

T___onto

Is definitely not

Might be

Definitely is

T is _____one-to-one

Is definitely not

Might be

Definitely is

nullity(T)

Is at most 1

At least 1

Must equal 1

Suppose that T : R* → R³ is a linear transformation and that T(1, 1, 1,1) = (0,0,0). Choose the option
that correctly completes each of the following statements.
• T [ Select ]
onto.
• T ( Select ]
one-to-one.
nullity(T) [Select ]

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.

Expert Solution

Step 1

Given: $T : R^{4} \to R^{3}$ is a linear transformation.

and $T (1, 1, 1, 1) = (0, 0, 0)$

since $T (1, 1, 1, 1) = (0, 0, 0)$

$\Rightarrow k e r T \neq \{0\}$

since $k e r \{T\}$ is not trivial.

hence $T$ is definitely not one-one.

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