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Q: ed Let R+R be a linear teanafonmation detined by Vind Ind the standard matiix A repeeseting L.

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Q: let M be the lebseque measure on B IR) Calcutate (1) Mes), where S = Where S= { Yn t h+3 i) M( n…

A: We know that measure of countable set is '0'

Q: Theorem-e Gaey-Hemiltion)let Aexz motrix

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Q: b) Evaluate the intergral. Show (with your work) that it is Cunvergent and give its Value or that it…

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Q: Show ALL WORK I. Find: dz a) for z=(x-y)5, x =5²t and y=st 2 b) dz for 2= (x-y), x=5²t and y= St

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Q: Find the area of theregion-thatis bqunded by the girencove and lles m the speafICd SECAET 2.

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Q: If X~ Unif (o,1) and YeaX+b~Unt (-I,i), ? then what are a,b a = ? b=? the values of a and b in this…

A: Probability distribution

Q: By means of Lagrange interpolation foomula, prove that 0.3 | -3 where (*)R = *R %3D

A: Given :- By means of Lagrange interpolation formula, y1 = y3 - 0.3 y5 - y-3 + 0.2y-3 - y-5 where yx…

Q: a420Provetthat the fortiaof22)+719tz) 5atsaContintontat

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Q: c) eval aie the to Il owing Integrai 3 n² +61 + 10

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Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

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Q: Show that if fis adifferentiable function, then Z:xf()Satis fies そ

A: Partial derivative and derivation

Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: Home uork: Let abeQ such that acb. Prove that HxE OK cbx

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Q: [S (x2 - Dx + 17) dx, = 7. (40.5) о The base b is: а) 20 b)22 с) 21 d) 23

A: First you have to know how to calculate base  Fisrt find D  then use the formula b = D * upper limit…

Q: EKample H (Z r) is Subring R de Sub ring (R,+

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Q: AD perpendicular to OF is not given , please prove also this

A: I am going to solve the problem by using some simple geometry to get the required result of the…

Q: U= 2i-35 j V = 59 +3

A: Given: u=2i−3jv=5i+3j

Q: Vove erf C-∞)= -I or J edt=-1 STT

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Q: What is the degree u = of the specified eement 33, F= Q (√3) u Over the Field F?

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Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: Prove that dv du 2 – u? + v² 18

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Q: 3. If y x +2 and u = 2x -1 then %3D du a) x b) 1/x c) 2x d) x/2 e) None of the above answers

A: Given that y=x2+2 and u=2x-1To find dydu

Q: Find the set the units of the integral domain Z [√5] = {a+b√-5: a, b € Z}.

A: Find the set of the units of the integral domain .

Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

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Q: Theorem-e Caley-Hemiltion)let Arxz motrix OAntra +detA=0 tet Azximufrix

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Q: Is Ź U Ź,asigma a lgebra over X? 4. Prove your an swer.

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Q: that uni, o wthat (h) 3.

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Q: (1+21)* (4– 31)* (3+ 4i)" (2– j)" 3. Given z = f ind the argument of z. a) –2.035 b) 2.035 c) 2.214…

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Q: Which is the correct formula for semi perimeter, SAS theorem for area, and SSS theorem for area?…

A: To find the correct formula :                (1).   semi perimeter.              (2).  SAS…

Q: Prove that Z Q has the universal property of inverting non-zero elements.

A: in Mathematics, Z is the set of Integers. and Q is the set of all rational numbers. Z→Q Let f(α)=1α…