12. Let T: R" Rm be a linear transformation. Determine if the following statements are true or false. Justify your answer by giving a proof or a counterexample. (a) If {v1, v2, V3} is a linearly independent set of vectors in R" then {T(v,), T(v2), T(v3)} is also a linearly independent set. (b) If {V1, V2, V3} is a linearly independent set of vectors in R" and T is one-to-one, then {T(v1), T(v2), T(v3)} is also a linearly independent set.
12. Let T: R" Rm be a linear transformation. Determine if the following statements are true or false. Justify your answer by giving a proof or a counterexample. (a) If {v1, v2, V3} is a linearly independent set of vectors in R" then {T(v,), T(v2), T(v3)} is also a linearly independent set. (b) If {V1, V2, V3} is a linearly independent set of vectors in R" and T is one-to-one, then {T(v1), T(v2), T(v3)} is also a linearly independent set.
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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Transcribed Image Text:12. Let T: R" R be a linear transformation. Determine if the following statements are true
or false. Justify your answer by giving a proof or a counterexample.
(a) If {v1, V2, v3} is a linearly independent set of vectors in R" then {T(v,),T(v2), T(v3)}
is also a linearly independent set.
(b) If {v1, V2, v3} is a linearly independent set of vectors in R" and T is one-to-one, then
{T(v1),T(v2),T(v3)} is also a linearly independent set.
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