* 1 -1 i -i J k - k 1 1 -1 i -i j k...

 

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* 1 -1 i -i J k - k 1 1 -1 i -i j k - k -1 -1 1 -i i -j j -k k i i -i -1 1 k -k-j j -i -i i 1 -1-k k j-j j j -j-k k -1 1 i -i i -j-j j k - k 1 -1 -i k k -k j -j -i i -1 1 - k -k k -j j i -i 1 -1 (a) Show that (i) 428 by showing that the left cosets of (i) are the same as the right cosets of (i). (b) Let : 28 → Z2 = {0,1} be a homomorpism. If ker = (i), write out the value of applied to each element of 28. That is, for all g € 28, find the value of (g). (c) Show that (-1) 28 (same method as (a)). write (d) Let : 28 → Z2 x Z₂ be a homomorphism. If ker v = (-1), (i) = (1,0), and (j) = (0, out the value of applied to each element of 28. -j * 1 -1 i -i J k - k 1 1 -1 i -i j k - k -1 -1 1 -i i -j j -k k i i -i -1 1 k -k-j j -i -i i 1 -1-k k j-j j j -j-k k -1 1 i -i i -j-j j k - k 1 -1 -i k k -k j -j -i i -1 1 - k -k k -j j i -i 1 -1 (a) Show that (i) 428 by showing that the left cosets of (i) are the same as the right cosets of (i). (b) Let : 28 → Z2 = {0,1} be a homomorpism. If ker = (i), write out the value of applied to each element of 28. That is, for all g € 28, find the value of (g). (c) Show that (-1) 28 (same method as (a)). write (d) Let : 28 → Z2 x Z₂ be a homomorphism. If ker v = (-1), (i) = (1,0), and (j) = (0, out the value of applied to each element of 28. -j

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