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

Q: 10. S= {r² + 3r +1, 2r? +r – 1,4r +1} is: a. a linearly independent set of P2. b. a linearly…

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Q: U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die that are…

A: Given If U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die…

Q: 2. Determine the power set p(A) = {{a, b}, {c}, {d, e, f}} 3. Suppose A = [7, e,0} and B = (0,1}.…

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Q: Let X-(1,0,-1,-V2)'. Then, |X|l2= Select one: a. 2 b. 1 C. 3

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Q: 4. Suppose X: SR has a countable range R. Show X = B/B(R) iff x-¹({x}) e B, Vx € R. €

A: Given:  A function defined with a countable range ℝ .   To show: X ∈ B/B(ℝ) iff X-1({x}) ∈ B , ∀ x∈ℝ

Q: If A₁, A, E and P(A) = P₁, P(A)= P₂, show that P(A₁4₂)≥ 1- P₁ - P₂. (Hint: Use DeMorgan's Law (44₂)…

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Q: E 27 F -> D] C. 44

A: Given : lenght  DC = 44, EF = 27 and AE = ED, BF = FC    To find : lengh of AB (x) ?

Q: Let A E RDXE, XE REXF, B € RFXD. Computed where g(X) = tr(AXB).

A: Let A∈ℝD×E, X∈ℝE×F,   B∈ℝF×D To Compute ∂g∂X where g(X)=tr(AXB)

Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

A: Our objective is given below:

Q: 1. Evaluate: e 3z I = dz (e² + e5z)2

A: given integral I=∫0∞e3zez+e5z2dz claim- evaluate the integral

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: (а b)с + (а - с)b + (с b)a 3 ve that v belongs to B.

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Q: and B =

A: (2/5,1/5,1/2)

Q: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

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Q: 10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What…

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Q: -1 15. Let A = 2 and B = Find X. A. [0 7] c5 기 В. D.

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Q: Q. Let X = {m, n}, and = {6, X, {m}, {n}}. Define the function Hn:E- (0, o0) by %3D Hn(A) ={ 3 if n…

A: measure theory

Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

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Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: If x-Gamm(a,B) and if a =1, then Gamm(1.B)-

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Q: Let f(x) = VT, 9(x) = ,. , andh(x) = x². (h o ((h o go f) – f)) (4) = %3D 5-x Select one: a. 4. 81…

A: let f(x) = x , g (x) = 45-x and h (x) = x2f (4) = 4= 2g (f(4) = g2= 45-2= 43h (g(f(4)) = h 43=…

Q: =gers and

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Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: Let U = x'e . Find dU .

A: The given function is: U=x2eyx Therefore: dU=∂U∂xdx+∂U∂ydy

Q: Y D Prox

A: Product of two sets

Q: Find the pro ection of v on the line with equation

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Q: 10. List the members of H = {x²|x = D₁} and K = {x € D₁ | x² = e}.

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Q: Let X B(25,0.2). E(X²) = Select one: O a. 41 Оъ. 29 О с. 25 O d. 0

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Q: Let S = (2,5]. True or false? VxSyy>x • A. True • B. False True or false? VxSy € Sy<x • A. True B.…

A: This is a question of Real Analysis. In particular it is a question from the real number set with…

Q: の dy Sーメ+ リーX +5

A: This is a problem related to differential equation. Based on the general formula we will solve the…

Q: 10. For V=2, fi , first find and and then, compute t+p%.

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Q: please include let u du substitutions

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Q: 8. Approximate 3.9996 using linearization.

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Q: Let X=(1,0, – 1,-V2)'. Then, ||X||2 = Select one: а. 3 O b. 4 C. 2 O d. 1

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Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

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Q: 2. If f(x) = 3x³ + 2, find a number c between a = -1 and b = 2 such that f(x) dx = f(c)(b - a) -1 A.…

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Q: 1. Let T-t(14) and P(-b <T< b) = 0.90. Then the value of b is A. 1.345 A В. 1.761 С. 2.624

A: We will tell you which one is the correct choice

Q: 2. If A = { € Z|18/x} and B = {r € Z/6/x} then ACB.

A: Introduction: Set A is said to be a subset of Set B If every element of Set A is also present in Set…