Answered: Let V and W be vector spaces and A : V…

Let V and W be vector spaces and A : V → W be a linear map. (a)The kernel of a linear map f : V → W is a linear one subspace of V. Prove that Ker(A), the kernel of A, is a linear subspace of V .

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 and A : V → W be a linear map.
(a)The kernel of a linear map f : V → W is a linear one
subspace of V. Prove that Ker(A), the kernel of A, is a linear subspace of V .

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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Step 1: Write the theorem for a linear subspace

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Step 2: Use the definition of Ker A

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Step 3: Use the theorem of step 1

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