9. True or False. Justify your answer. (A) Let T : V → W be a linear transformation and {v1, · · , Vn} be vectors in V. If {v1, ·. , 'n} is a linearly independent list in V, then {T(v1), · · ,T(vn)} is a linearly independent list in W. (B) The linear transformation T : P2(R) → M2×2(R) defined by - C T(a+ bx + cx²) || - C C - a is an isomorphism.
9. True or False. Justify your answer. (A) Let T : V → W be a linear transformation and {v1, · · , Vn} be vectors in V. If {v1, ·. , 'n} is a linearly independent list in V, then {T(v1), · · ,T(vn)} is a linearly independent list in W. (B) The linear transformation T : P2(R) → M2×2(R) defined by - C T(a+ bx + cx²) || - C C - a is an isomorphism.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![9. True or False. Justify your answer.
(A) Let T : V → W be a linear transformation and {v1, · · · , Un} be vectors in V.
If {v1, ·.. , 'n} is a linearly independent list in V, then {T(v1), · . , T (vn)} is
a linearly independent list in W.
(B) The linear transformation T : P2(R) → M2x2(R) defined by
-b b-c]
6 –
а
T(a + bx + cx2)
— с с— а
С —
is an isomorphism.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2F38aeb9f8-d6f3-4d86-a0ec-fccd20ebc7be%2Fpt8slvf_processed.png&w=3840&q=75)
Transcribed Image Text:9. True or False. Justify your answer.
(A) Let T : V → W be a linear transformation and {v1, · · · , Un} be vectors in V.
If {v1, ·.. , 'n} is a linearly independent list in V, then {T(v1), · . , T (vn)} is
a linearly independent list in W.
(B) The linear transformation T : P2(R) → M2x2(R) defined by
-b b-c]
6 –
а
T(a + bx + cx2)
— с с— а
С —
is an isomorphism.
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