V is a 4-dimensional vector space with basis B = (v1, V2 , V3 , V4). T:V → V is linear transformation with rank three and satisfies T(v1) = v + v2 +- v3 + v4, T(v2) = v1 + 2v1 + 3v3 + 4v4, T(v3) = v1 + 3v2 + 4v3 + 6v4. If T(v4) = v1 + 4v2 + 5v3 + avĄ what is the value of a? 8 O 7 O 5

V is a 4-dimensional vector space with basis B = (v1, V2 , V3 , V4). T:V → V is linear transformation with rank three and satisfies T(v1) = v + v2 +- v3 + v4, T(v2) = v1 + 2v1 + 3v3 + 4v4, T(v3) = v1 + 3v2 + 4v3 + 6v4. If T(v4) = v1 + 4v2 + 5v3 + avĄ what is the value of a? 8 O 7 O 5

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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Question

V is a 4-dimensional vector space with basis B = (v1, V2 , V3 , V4).
T:V → V is linear transformation with rank three and satisfies
T(v1) = v + v2 +- v3 + v4, T(v2) = v1 + 2v1 + 3v3 + 4v4, T(v3) = v1 + 3v2 + 4v3 + 6v4.
If T(v4) = v1 + 4v2 + 5v3 + avĄ what is the value of a?
8
O 7
O 5

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