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posted by  nyx on 11/3/2009 3:23:16 PM  |  status: Closed  |  Earned Karma: 25

isomorphism 2

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Linear Algebra linear algebra by jim hefferon three 8 11/3/2009 at 5:00:00 PM
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i need more help with isomorphism please will rate high! thanks


2.8 Decide if the spaces are isomorphic. 

(a) R2 , R4 

(b) P 5 , R5 

(c) 

M 2 ×3 , R 6 

(d) 

P 5 , M 2 ×3 

(e) M2×k , C^k
-nyx-
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posted by GUNSH on 11/3/2009 5:48:08 PM  |  status: Live
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(a) R2 is a vector space of dimension 2 and R4 is of 4.
two vector spaces are isomorphic if their dimensions are equal.
so, R2 , R4 are not isomorphic.
(b) p5 means the set of all polynomials of degree 5 .
so, its dimension is 6.
it cannot be isomorphic a vector space of dimension 5 which is odf  R 5
(c) by assigning  we can show the isomorphism between P5 and M2x3.
 ( e) is an isomorphism between  the space of matrices with dimension 2k and the set of complex numbers of dimension k.
GUNSH,you are free to send message if you are stuck anywhere in this solution
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posted by nyx on 11/4/2009 8:21:01 AM  |  status: Live
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thanks. was wondering if you can help me with another question. i posted it here on Q&A board too "image of domain/isomorphism" is the title of the question.

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i need help also with this question. i don't know how to start. will rate high thank you

consider the isomorphism RepB ( ·) : P 1 → R ^2

where B = ?1, 1 + x?. Find the 

image of each of these elements of the domain. 

(a) 3 − 2x;

(b) 2 + 2x; 

(c) x 
-nyx-
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