8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ = (2,0, c = { ₁ = (₁ 3₁3), U₂ = (0), 3' D = (U₁ = (0₁) ₂ = (0, c) C, d) D. a) A, b) B,

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A: Solution is uploaded in the image in scanned form.

Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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A: Given,

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A: The given equation is; 3u"-u'+2u=0, u(0)=2,u'(0)=0

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A: Consider the given equation.

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A: To find: Z/(5)

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Q: 12.) Let h: IR³ -> IR5 and g: IR² -> IR³ be IR² -> IR³ be given by hcxy. 2) - (xyz, ex* x sin(y),…

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Q: 3 0 -2 3-Let A= 0 1 2, B= Find:- 3 L-1 1 5] (2A – I)B' and show that (BA)'=A'B'

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Q: P(E2) = P(E3) =s, P(E4) = P(E5) =/20, P(Es) = '/10, P(E7) = '/5: A В E1 o E 2 o E4 E5 o E3 o E7 O E6

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Q: Q4. (a) Give A = 2xy â, +3â, +z'yâ,, calculate v.AdV as shown in Figure Q4(a). A, (0, 1, 1) (0,0, 1)…

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A: Solution- Given that X~U(-1 , 1) Then Y=3X-1~ ?

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A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: (kx 3. -){(kx-ky +kz).

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Q: O a. 1-1/e O b.0 O c. 1+1/e O d. Divergent O e. 1

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Q: 3 If = u(1) = () a1 du dt ° ) u(t) where a2 u1 (t) and u1 (t) = B1e + B2et u2 (t) %3D and u2 (t) =…

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Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

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Q: Prove that H(x, y) = (x, –y) provides a conjugacy between 1 X' = 1 X and Y' Y. 1 1 1 1

A: We are Given that :  H(x,y)=(x,-y) X'=11-11X , Y'=1-111Y The Matrix H is corresponding to the…

Q: 2.) Find a general set of solution vectors of x'1=-5x2 x'2=x1+3x2

A: To find the general solution of a system of linear differential equations, follow these steps: 1.…

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A: The given function is

Q: (A) Given that n(A')=20, n(B')=40, n(A'∪B')=50, n(∪)=80, find A ∩B (B)  Given that n(A')=70,…

A: A)n(A')=20n(B')=40n(A'B')=50n(U)=80