5. Show that SL(n, R) is a normal subgroup of GL(n, R). Further, by apply-ing Fundamental Theorem of group homomorphism, show that the quotientgroups GL(n, R)/SL(n, R) is isomorphic to the multiplicative group (R\ {0}. -)of non-zero real numbers. (Here GL(n, R) denotes the general linear group ofall n x n matrices over R and GL(n, IR) denotes the special linear group of allnxn matrices over R.)

Suppose, ϕ:GLn,R→R\0 such that ϕA=A for all A∈GLn,R Now, sinceA∈GLn,R if and only if A≠0 Now, we see…

Answered: Show that SL(n, R) is a normal subgroup…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 23E

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