IITM BS Question 32 - Week 6 Practice

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IITM BS Question 32 - Week 6 Practice | Prasnya

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Q32Comprehension1 Mark24 Mar 2024

Passage

Let

V

and

W

be two vector spaces. Suppose there exists an isomorphism

T

from

V

W

. Based on the above data, answer the given subquestions.

Is the statement true or false? Let

\{u_1,u_2,u_3\}

be a subset of

V

. If

\{T(u_1),T(u_2),T(u_3)\}

is linearly independent in

W

, then

\{u_1,u_2,u_3\}

could also be linearly dependent in

V

Q32

00:00

24 Mar 2024

Mathematics 2 · Week 6

Q32.Is the statement true or false? Let

\{u_1,u_2,u_3\}

be a subset of

V

. If

\{T(u_1),T(u_2),T(u_3)\}

is linearly independent in

W

, then

\{u_1,u_2,u_3\}

could also be linearly dependent in

V

.@passage

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