6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T. %3D %3D

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

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

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Q: 4/ur grans funthon y"-Uy't3y = et

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Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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Q: 2. Prove that there are no rectangles in S2. More precisely, prove that if A, B, C, D E S² form a…

A: Given: ∠A=∠B=∠C=∠D=π2

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: Icm(a, b) = ab if and only if a and b are relatively prime. %3D ylgn O ihi O

A: True

Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…

A: Using Green 's theorem line integral to double integral

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A: Subspace of the vector space

Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

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Q: 9- Show that H= {0 E S6=(6)o = 6} is %3D subgeoup of and find its wight cosets S6 ets left Casets ·…

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Q: Solve the differenlial =* +y+Xy equa lion with initial condilion yco) = -I , andOSK<2 with step long…

A: Given y′=dydx=x2+y+xy, y(0)=-1,h=0.4Here, x0=0, y0=-1, h=0.4 , xn=2

Q: 4.51 Verify that BIBD with the parameter a = 8, r = 8, k = 4, and b = 16 does not exist.

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Q: Solve the loieal Vahue Pr blem by the characteristic Hethod Using For a) flx)> 1 and A fx)- K.

A: Solve intial value problem Solving by characteristics equation

Q: 5. Let H= [ (û ¿)I a,b,c EIRI, show that: (H,+) is a sub gromp of (M,+).

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Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: Show that the intervals S [1,3] and T =[2,8] are equinumerous by finding a. bijection between them.

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Q: Show that every positive sol fron of Ay + B, k=osl,2- & bosunded, %3D JK is i-e, ogy sB-if A<1. 1-A

A: Given yk+1=Ayk+B, k=0,1,2,... Then the objective is to find the solution at which the sequence is…

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: 4. Find the uolume of the following objects : side dengtn a) A cube with ane síde lenpth ña" "ll b)…

A: (a) The volume of the cube with side length a is given as follows:

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

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Q: Suppose that X,Y, Z CU. If n(U)= 37, n(X) = 19, n(Y) = 11, n(Z) = 16, n(X nY) = 8, n(X n Z) = 12,…

A: NOTE: A is X, B is Y and C is Z.

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: 3. Show that X = (x|Ax=b, x ≥ 0} is convex. following ure which no

A: As per our guidelines we are supposed to answer only one question.

Q: 40. In isosceles AMNP, MN = MP. With point Q on MN, MO = QP = PN. Find mZM and mZN. Q 384.

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Q: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

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Q: 7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices…

A: Greens theorem

Q: Find the absolite marima and minima points between [o,u] gf y : * + 2dx' sunchion is porsbl.

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Q: Select all the Points through which a unique solution for the DE ,2 y? IS nySot eed by the Existence…

A: Given differential equation is y'=13-x2-y2

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: => For The Wbech Ualuo of E doas the Martrix イK %3D have one roal eaomalue of Mutiplicty?? k =

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Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

Q: (2.13) Compute Lp(t), where P is the regular tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1),…

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Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

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Q: 5. If 4=2xy į +3x°y -3pyzk is solenoidal at(1,1.1). Find p.

A: DivA=0

Q: In AJKL, JL is extended through point L to point M, MZLJK = (x + 9)°, mZJKL = (x - 2)°, and m/KLM =…

A: The exterior angle is equal to sum of two opposite interior angles. We will use this property to…

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.