Given the following sets, perform the indicated set operations: U= {a, b, c, d, e, f, g. h, i, j, k} A = {a, b, c, d, f, i} В %3 (а, с, е, g} C = {b, d, f, h} a) AN (Bu C) b) (AN C)' - B C) (A - C) N B' d) в X (С - А)

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Q: 1. Given : %3D 13 4 -6 -4 8 5 4 24 4 12 2 A = B = 8 -S 4 6. 4 6. 2 3 2.

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Q: Let a E Z. Prove that if a = 2 (mod 6), then a? = 4 (mod 12).

A: We will prove this by basic result of congruence

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Q: a) Describe the kernel and the image of Jn. (b) Use this to show that ??Jn is diagonalisable when n...

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Q: X1 3x, = -2 Зх, + х, — 2х, — 5 2х, + 2х, + х; —D 4 2x3 X3 =

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Q: Let Mn(R) be the set of n x n matrices with real entries. Define the sets V1 = {A € M2(R) | A = A"} ...

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Q: a) Draw a graph of f(t) and determine ∫_(-∞)^∞▒|f(t)| dt  b) Write the Fourier integral representati...

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