Prove S^2 is simply connected.

Q: Without doing any calculations in Aut(Z105), determine how manyelements of Aut(Z105) have order 6.

A: Given: Automorphism, AutZ105To find: Number of elements of AutZ105 having order 6.

Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: Draw the Venn diagram with the following information: ANBNC={√2, √-1}, (ANB) NC'={2%, 00}),…

A: Here we eight disjoint parts , putting into them we can construct ven diagram

Q: Find the midpoint of AB if A(-3, 8) and B(-7, -6)

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Q: Bolve * LOB3X + 3inxt é Ars: 1 = De B o83X -3_8in2 18 3x m , 18

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Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: 2 ľ xe2xdx

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Q: 1 0 -2 0 0 0 1 0 0 0 0 0 0 3 1 0 0 1 0 0 0 0 0 0 0 1. Assume that A~ 0 -4 1

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Q: 6. (6x – 15)' (2r+ 1)

A: To find x ?

Q: Consider that: 1 + 2 + ... + n = An^2 + Bn + C  For all n and for some constant A, B and C.…

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Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: f U1 and U2 are both upper triangular matrices, and L1 and L2 are lower triangular which of the…

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