Answered: Let V and W be vector spaces over a…

Let V and W be vector spaces over a field F, and let T : V → W be a linear transformation. Suppose that dim(V ) = 6 and dim(W) = 7. What are the possibilities for the pair (rank of T,nullity of T)?

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

Let V and W be vector spaces over a field F, and let T : V → W be a
linear transformation.
Suppose that dim(V ) = 6 and dim(W) = 7.

What are the possibilities for the pair (rank of T,nullity of T)?

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