1 6 [: 2. Let %3D matnix c (by tnial and erron) Constauct a C (by tnial and eror using anly !,-1 and 0 entries such that as note that AC713 CA = 12, Compute AC and

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:…

Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

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

Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: 1 and that p= V3 1 + k 1- k' Given that k = express in its simplest surd form (i) P, 1 (ii) P :-

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Q: A The legih in pnefers of the fout sider f a building angx Cox- 5-9*, and Axt a. Calculate The…

A: Solution :   (a)   Total length around the building               = 3x + (6x - 5) + 9x + (4x + 1)…

Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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Q: 2.6. In the text, the modulus is defined in terms of the inner product. Prove at this can be turned…

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Q: A) Show that the surtace x-2yz ty' =4 is orthogon al to any of the sm tamily of sur faces…

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Q: Which of the following would not be sufficient information to conclude that AXYZ is similar to AMNO…

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Q: 4. Exercise §5.2 #20 [This exercise presen Theorem 5.9 using the Möbius Inversion Form to that in…

A: Given, d be a positive divisor of p-1. To prove that                            f(d)=ϕ(d)

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: Find the rank of A= = xS+ x + invertible. [exham S] O A MOITERUD 225 10-4 and explain why it indic 4…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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Q: Prove that 1/(nx) → 0 pointwise, but not uniformly on (0,1) as n → co.

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Q: 우(4,3) - +xy Elewhere a fivd 우 (s) 6) find p( ys%2 /x= 0:3)

A: A joint probability distribution gives the probability for two variables together which is…

Q: 6.1 let T be a l'iner transformatio from Mga into M,a Sub that %3D

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Q: 2.9 Give the joint (bivariate) cdf of X and Y, Fy(x, y), in tabular form. (Copy and complete this…

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Q: Janily of or edo thogonddraje to the following formily': x²- axy + Cy =36

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Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

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Q: 7.37. U₁, U₂ are independently and uniformly generated between 0 and 1 by a machine. Let X denote…

A: Given that: U1 and U2~Uniform0,1 Sum, X=U1+U2 Let Y = 1- U2

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: 20.* a. Let P(z) = 1 + 2z + 3z² +.. of P(2) are inside the unit disc. + nz"-1, By considering (1 –…

A: Proved by using Rouches theorem from complex analysis.

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: 2 1 Find a mat rix P such that P- 2 0 0 3 0 3 [11 O AP = 1 0 -1 0] BP = 1 1 1 1 OCP = 0 1 1 -1 ODP =…

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Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: (2) Show that if dim(V) = k (so in particular, T has k distinct cigenvalues), then there exists v e…

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Q: 5 Suppose Te L(V), m is a positive integer, and v eV is such that T-v0 but Tv=0. Prove that v, Tv,…

A: According to the given information, Suppose that:

Q: Show that following MA models are equivalent A: Yt = et – Oet-1 for et ~ WN(0, 1) 1 Yt = et for et ~…

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Q: SSR is defined by SSR = E9 - 9). Prove %3D (1) SSR = 3} S.z- (2) E(SSR) = o + Bị Sr. (3) Show MSR ~…

A: Given, SSR=∑i=1ny^i-y¯2. The fitted equation of yi=β0+β1xi+εi is  y^i=β^0+β^1xi, for i=1,2,...,n. yi…

Q: 1. Compute the following double in- tegrals. a. SSr 2x + 4y + 10xy dA, R : 0 < x < 1,0 < y< 2

A: Given that  The double integral 2x+4y+10xy To evaluate the double integral using the given…

Q: If a (b,v,r,k,lambda) design is symmetric with lambda=1, then there exists an integer n such that…

A: Using projection property in BIBD.  We know that, Symmetric 2-designs with λ = 1 and order n &gt; 1.…

Q: 6) let fl2) = CosCitaiy) 22atey Express flz) that f satisfies in the form and fornd z So the Canchy-…

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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: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: (2) Let f(x) = cos (2x). Find the Hermite interpolation H3(x) using xo = 0 and x1 = , and use error…

A: Given: fx=14cos2x We have to find the Hermite interpolation H3x using x0=0,x1=π4…

Q: Evaluate the integral. |csc 37t dt 1 O A. 1 csc 7t cot 7t- In |csc 7t + cot 7t| + t + C В. 14 csc 7t…

A: givenI=∫csc37tdtrewriteI=∫csc27t.csc7tdtwe know trigonometric…

Q: 1. Obtain the weak formulation for the following BVP: in Ω, -V (kVu) = f u =g on ô0.

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Q: In GL(2, Z,,). det

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Q: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

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Q: 7.1) 19) Evaluate the integral.

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Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

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Q: 3. C-1) " Conditionally absolutely codvergent divergent. Con vergent, 2n+ Sinin) or

A: Solve the following

Q: 5. Let A z 3 4 87 8- ーん Prore that find ite diogonel form. A it diaganalianllen and

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Q: In C[0, 27], with the inner product -2 (f, 8) = | f(x)g(x) dx, show that the set S = {1, sin x, cos…

A: Given: Inner product defined as: &lt;f,g&gt; = ∫02πf(x)g(x)dx To show that the set S = { 1, sinx,…

Q: In Z[V-5], the element 29 is: None of the choices Irreducible Unit reducible

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Q: Consider x1 = (I11, F12)" and x2 = (12n,I2)". Let x = (x}, x})T and IPPP 1 P P Cov(x) = PP1p PPP1…

A: The  first pair of canonical variables, or  first canonical variate pair is the pair linear…