Prove that : a"+ (a+ 1)° =1 +a(1+い) (mod a la+s) for all a, m,n E Z.

Q: Prove the following: If ā and b are in R', then (5 -a)×(5 +a)=-2(āxb).

A: Given a⇀ and b⇀ are in R3. To prove :  b⇀-a⇀×b⇀+a⇀=-2a⇀×b⇀

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: 4. (а) Let a, b, c E Z. Prove that, if a | b, then ac | bc, but that the converse may be false. (b)…

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Q: If A = [a] and Oa=c+d 01+d+a-2c=0 O a=1-d+c and B = -61 . Determine the condition for which det (A +…

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Q: Suppose ū = 2j + k, ū = 2i – 4j + 2k and w = -5i – j+ k. %3D Compute the following values:

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Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: If u = (3,0), v = (1,2), and w = (1, –1), find a and b such that u= av + bw b = (enter numerical…

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Q: If u = 7 then uu? and u'u =

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Q: .    Verify that: a)    (A - B) – C = A - (B ∪ C) b)    (A Δ B) ∩ B = B - A

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Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: Q24 prove that b) 3i 3i √2+i √2-i = 2 ?

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Q: Please help me with this question. I am having trouble understanding what to do. Please show all…

A: The objective of the question is to prove that the sum of the kth powers of the first n natural…

Q: xercise 4.2.9 Repeat the steps of the previous example where ad |) = 1/2, -42²) 3 1+2i -29] 1-2i -1…

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