-6 12 =[{]• .Determine if w is in Col A. Is w in Nul A? Let A = and w =

Q: (1) Ø° = Ø and M° = M. (2) If SST, then S° ST°. (4) S is open if, and only if, S = S

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: 11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If…

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Q: 2. By writing /12 = (7/3)-(7/4) and considering e/12,evaluate cot(7/12) and tan(z/12).

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Given that a =3 and 1 if a is even; a n+1 5а - 1 if a_is odd. Then tern number four, i.e., a а, is

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Q: 2 Let A | and U = H. Then A2017U is equal to = ... A) B

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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: Let a, b, x E Z be given. Show that: ax + 6 even (x odd Vb ev en )

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Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: Let 2E An and BE Sn show that Hhen Baß'E An.

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Q: 200 ra, is 25a 200 200 Let (1+ x+ x*) = Ïq,x and a = Ea, , then value of

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Q: 2. If A C B, then m*(A) < m*(B). 3. If A = Q' n (0,1), then A is measurable. %3D

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Q: Suppose gcd(a, b) = 1. Prove that if r|a and s|b, then gcd(r, s) = 1

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Q: prove that: DO e de a e +6 2/3 cwhere a, b > o

A: Where a, b&gt;0

Q: 1. Let P(A) = 0.4 and P(AUB) = 0.6. For what value of P(B) are A and B independent?

A: To find The value of P(B) such that A nad B are independent

Q: Suppose, X-Binom(m.0) and 8- Beta (a, B), then E(X) is equals to, b) d) maß aß ma α+ B me Answer B €…

A: Given: X|θ~Binom(m, θ) And θ~Beta(α, β) Formula Used: X~B(n, p) E(X) = np To Find: E(X) = ?

Q: Let S = {1,2,3,4, 5}, G = {(1),(123), (132)}. For each element %3D a e S, find stabc(a) and orbg(a)

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Q: 1.1 Let z, w e C. Show that |z + w? + |2 - w? = 2(|:|2 + |w?).

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Let S = {z € C| 26 = 1}. (a) For each element w in S, find def. {w°, w*, w?, w³, . ..} and then…

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Q: az + b If T(z) cz + d a, b, c, d e R. Show that T(RU{∞}) = RU {∞} if and only if exist

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Q: $ = g(ø, v, ø) = aø + - b = g(4, 4, 4) = arb + which can be rewritten as ayoy – ado? + Bo², ayoy –…

A: Given: ϕ=gϕ, ψ, ϕ=αϕ+βϕ2γψ-δϕ and ψ=gψ, ϕ, ψ=αψ+βψ2γϕ-δψ To show: δ1-α+βϕ2-ψ2=0

Q: 1. Prove: Va, b, c E Z: alb and blc = alc 2. Give an example with a = 7 and b, c + 7.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: 2, Say whether the Runction is even, odd, or neither. Give reasanS for your dnswer. ga) = x"+ x*-1

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Q: Suppose A C B, a E A, and a ¢ B – C. Prove that a E C.

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Q: for AUB unih AG B inderser for is not unusual.) Then, A+B= B+ A A B= B A A (B+ C) = A B+ A C A+Ø= A…

A: In this question we need to explain about the underlined symbols ∪ ,   ∩  ,   ϕ  .

Q: Let E L-5,20), be ine universal y- C-2,4] and z-G,10] Se t and be tne Subets op E. Find En (y-Z)ot

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Q: 1. If l = P+[v]=Q+[w] , how must P, Q, v, and w be related?

A: Given l=P+[v] is a line where [v] is a span of a unit vector v, we can write [v]=cv, c is a scalar…

Q: Given u = (5,0, 0) and v = (5, 5, 0), which of the following represents u x v?

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Q: 5. If A e U(n) and A e C has length one, show that XA € U(n) .

A: If  A∈∪n and  λ∈ C  has  length one,show that λ A∈∪n.

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

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Q: (10) If H < Z» × S, with |H| = 12, then H = %3D

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Q: For the following Venn diagram, what is p{(AU B)C}? C. 0.24 0.06 0.08 0.04 0.23 0.23 0.07 A 0.914…

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Q: Given: j ll k, <1 ~= <3 Prove: n ll m

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Q: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

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Q: Let A € M₂, (C). Then, for a E o(A), GEO.MUL(A) ≤ ALG.MUL₁(A).

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Q: 5. Let M(x, y) be "x has en all students in your class. Use qu There is a student in your class v or…

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Q: Let T, >0 be given. S

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Q: Given that a, =3 and if a is even; a 5a -1 if a is odd. Then tern number four, i.e., a, is

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Q: 13 13.150lve the sys Jordan elin 2x

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Q: - [ then C(A) = N(A) if: 13. If A %3D A. a, = 0 B. a, = 2 C. az = 1 D. a, = -1 an suer %3D no

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Q: Let X1,., X, N(u, o?). iid N(H, o?). Find E(), if ju = X1 + (X2 + + X(n %3D 2(n-3) 17 16 4 O 17(n-2)…

A: Given that, E(X1)= E(X2)= ......E(Xn)= mu

Q: and y If a = , then x = ||

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Q: Let A, B and C belong to M(3,R) such that: det(A) = 10, det(B)= 10/5 and det(C) = 3, then…

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Q: -6 Let A eponvalve, k mut For A to hove an 7. be 2.

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Q: [:! -8 -2 -9" 27 1 Determine if w is in Col A. Is w in Nul A Let A = 4 8 Jand w = 4 64

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Q: For AABC with medians AD, BE, and CF, let m = AD + BE + CF, and let s = AB + BC + CA (Fig. S3-13).…

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Q: (vi) P= Q = (P(N); C), and o defined by {1} if 1 € U, {2} if 2 € U and 1 ¢ U, p(U) = otherwise.

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Q: Let A = 10 0 1 1 -8 2 -1 1 -2 -21 2 -2 6 0 0 -2. and w - 13 2 0 2 [2] . Determine if w is in Col A.…

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Q: (1) -) Let o, t e S6 such that 1 2 3 45 6 1 T = 3 4 and 6. 4 3 5 1 2 1 6 5 4 Determine the…

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Q: Hw/O Find Adi A if A. O kind Adj A il A=

A: (1). The given matrix is:  A=521  314  463