Please see attached photo. Im not sure how to use the properties of isomorphism to prove the composite function is 1-1, onto, and has the homomorphism property. : S' + S" is an isomorphism of (S', '): S- S' is an isomorphism of (S. *) with (S', ') and"), then the composite function y o p is an isomorphism of (S, *) with (S", ").27. Prove that ifwith (S".

: S' + S" is an isomorphism of (S', ') : S- S' is an isomorphism of (S. *) with (S', ') and "), then the composite function y o p is an isomorphism of (S, *) with (S", "). 27. Prove that if with (S".

: S' + S" is an isomorphism of (S', ') : S- S' is an isomorphism of (S. ) with (S', ') and "), then the composite function y o p is an isomorphism of (S, ) with (S", "). 27. Prove that if with (S".

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 28EQ

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Question

Please see attached photo. Im not sure how to use the properties of isomorphism to prove the composite function is 1-1, onto, and has the homomorphism property.

: S' + S" is an isomorphism of (S', ')
: S- S' is an isomorphism of (S. *) with (S', ') and
"), then the composite function y o p is an isomorphism of (S, *) with (S", ").
27. Prove that if
with (S".

Expert Solution

Step 1

Since, phi is an isomorphism, it is one-one onto homomorphism. Thus, it is bijective. Similarly, Ψ is bijective. Hence, their composition is bijective.

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