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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 .

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 .

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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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 .

 

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