3. (i) Show that e = is an idempotent in M2(Z12). [3 Marks) (ii) Give an explicit description of the splitting of Z>2 gi

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3 I Show That E Is An Idempotent In M2 Z12 3 Marks Ii Give An Explicit Description Of The Splitting Of Z 2 Gi 1 (59.64 KiB) Viewed 25 times

3. (i) Show that e = is an idempotent in M2(Z12). [3 Marks) (ii) Give an explicit description of the splitting of Z>2 given by the idempotent e of part (i). 16 Marks] (iii) Consider the left Z-modules Z2 and Z, and let g: Z2 +Z be the epimorphism g(a,b) = 4a + 76. Find a morphism f : Z → Z? such that 0 + Z → Z2 97 Z+0 is exact. (iv) Is this sequence split or not? (5 Marks [2 Marks