3. (i) morphisms State what it means for a sequence of left R-module MNPQ to be "exact". (ii) Let f: Z² Z² and g: Z² → Z be the morphisms given by f(a, b) = (2a + 3b, 6a +9b) and Show that the sequence is exact. g(x, y) = y-3x. z²Z²Z-0 (iii) State what is meant by a "short" exact sequence, and what it means for a short exact sequence to be "split".

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Q: (3x € X: (Vy € Y : E(x, y))) = \x € X : (³y €Y : ¬E(x, y)) ¬(Vx € X : (³ € Y : E(x, y))) = (3x € X :…

A:

Q: Find matrices P, D, and P-1 that diagonalize matrix A, where A P- D P-1 62 88 -48-68,

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.