Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n-1, 12n+1]}, be a family of elements of B(R). u(U 1 in=1]) equals n=1 4n-1 n=D11 72 a.i b.5

Q: Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (х, у)…

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Q: Determine z and y such that -3 31 x y 2 47 -1 %3D -1 -2 2. -3 2x+y 3

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Q: Consider the function d: Z6 → Z6 defined by d(x) = 2x mod 6. Select the true statements: d is…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [ Then u(Un+l in 1) equals a.1 7n-1…

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Q: Let Þ(u, v) = (7u + 9v, 9u + 2v). Use the Jacobian to determine the area of $(R) for: (a)R= [0,9] ×…

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Q: Let X1,., X,id N(u,02). Define a =X1 +X. Find the bias ofu. (b) H (a) (c) u 5 3 (d) (e) None

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Q: Determine all s ∈ R such that I4s= (I4)s

A: Given I4s=(I4)s We know I4=1 I4s=(1)s

Q: ey 2 In (Z5 x Z5, +5,-5) the set B = {(2n, 2n), n E Z5) is a subring.

A: Here given ℤ5×ℤ5, +5, ·5 is a ring, Also given  B=2n, 2n: n∈ℤ5, Since ℤ5=0, 1, 2, 3, 4 thus B=2·05,…

Q: Suppose n E N and u, v € V₁ such that |u| = 5, |v|= 4 and u⚫v=-7 Find |3u + v. Find t R such that u…

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Q: Let o+ a eR and let G= {na| nez} ,then (G, +) is an abetian gronp. ( Hint: the identity element is…

A: Let 0≠a∈R and let G=na|n∈Z, then G, + is a group if the following properties are satisfied. 1.…

Q: 2. Let f: ZxZ-ZxZ be defined by f(m, n) = (3m+n,n²) a. Is fone-to-one? b. Is fonto?

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Q: 3.6-3. Let X, X..Xs be trom a chi-square distributic -1 and e 2. (a) How is Y SX distr 18

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Q: Prove that (n – 1) +n° + (n + 1)° is divisible by 9 for n E {1,2,3, . }

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Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [Tn-1 12n+1]}, be a family of…

A: Please Check the answer in next step.

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

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Q: b, c e R such that abc

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Q: Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["±1, 4n=1]}, be a family of elements…

A: Consider the provided question, Let X, BR, μ be a Borel measure space. Suppose that An=n+1n,…

Q: Let xer" and ge I show that =yex is an imer product.

A: I have to show that the given relation satisfies three conditions to be a inner product

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: 1. Evaluate the following commutators: a) [p, x5] b) [cos kx, p]

A: These are the questions from the operator theory.

Q: If 4 p and q P крса are conjugale exponent a measure X a measure space, p р. f₁g:x [₁₂+] measurable…

A: Given P and q are conjugate exponent and f,g are measurable function and let p,q∈(1,∞)

Q: Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and |q| for…

A: In this question, concept of inner product is applied.

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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Q: In this task there are two situations: one dealing with counting toothpicks and the other dealing…

A: We need to justify the nature of the relationships among the data points whether it is discrete or…

Q: Which of the following notations given below is NOT equivalent to ? ni Note: There is a 'double-dot'…

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Q: Find the g.c.d. in Z [i] of 2 and 3 + 5i.

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Q: Find the area of JEN if the coodrinates of the vertices are J(0,3) E(6,0), and N(8,3)

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Q: 3. The Wronskian of {x 2,x 2} Select one: а. 3 5. b. x С. Х d. i5/2 m/N O O O

A: The Wronskian(W) of two differentiable functions f(x) and g(x) is given by the equation;…

Q: 2a In R^ show that : 2 as 211x11² + 211|4|1²³ = || Xx+y|11² + 11x-y₁1² ( This is known a the…

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Q: Show that ▼ƒ(x) = ["* V²ƒ (x + 7(y − x)) (y − x) dr. - Show all your work pls.(readable…

A: We will use the basic knowledge of integral calculus and vector calculus to answer this question.

Q: Evaluate f (x + y − z)² dV for the box B with dimension: [0, 6] × [0, 4] × [0, 3]. (Use symbolic…

A: Solution :-

Q: Suppose that A and B are two sets such that n[A] = 5, n[B] = 9, and n[AU B] = 13. If n[U] = 19, then…

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Q: 2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c…

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Q: Let V O The line x+y=2 O The line x+y=1 O The line x+y=0 O The line x+y=-1 O The line x+y=-2 = R²…

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Q: 10 1301 The dimension of N(AL the null space of A = 0 2000 1 is 10141 1 [202602. O a. none of these…

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Q: Evaluate f (x - y)(y - z) dV for the box B3 with dimension: [4, 9] × [0, 1] × [0, 1]. (Use symbolic…

A: We have to evaluate the integration .

Q: ACTIVITY 2.22. Let C = {x, y, z}, D = {a, ß}. List all elements of: (a) C x D, (b) D x C, (c) C x C,…

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Q: Rinding Construcding Al or 2 3 A z → (AII) (AIT)

A: The given matrix is: A=12310-1231 To find its inverse.

Q: Let (X, B(R), µ) be a Borel measure space. Suppose that {An = [In-1 12n+1]}, be a family of elements…

A: Given, An=7n-n,12n+1nn=1∞ We need to find the value of μ=Un=1∞n+1n,4n-1nn=1∞

Q: Q5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["+1_ 4n-1 Show that A1 C A2 C…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.