6) Suppose z,=4¿ and z,=32 & Z2 Give Z1 7) Give the value of 5! and also show the calculation done to obtain it.

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Q: 3. cooficiant af z" in the apransion 3)11

A: From the Binomial Expansion

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A: We have to prove given equation.

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Q: Suppose 2а, 1— 8а, 2 + 5а, -з ат and 55, 57, =296 a4= a5= a6 Find a1, a2, and az. = ID а2 аз

A: From the given information,

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Q: 12) a-:]- B-[:: ind AR 3 0 3 -2 1 Find AB. %3D -2 1 0 4-3

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Q: 5|8" – 3", Vn EN

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Q: 3. prove that: det (AB) det (A) det (B) If A -(:), = - ( :) B = 7 2

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Q: By 2 Cas X the Same. way prove that

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Q: 4, Suppose P(A) 2 0.8 and P(B) > 0.5. Prove P(AN B) > 0.3. Hint: You may use P(AUB)< 1.

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Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? If p|rq, prove that p|r…

A: Given that p, q and r are prime numbers and p≠q.

Q: 8. Following the idea of Exercise 6 and referring to Exercise 7, express the positive gcd of 49,349…

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A: This question is about set theory