[100] 1 [1 0 0 5. IfA = |0 a) Av B b) ΑΛΒ c) ΑΘΒ [1 1 1] o 1), find 0 1] 1 and B=Jo [1

Q: Let u = Al 2 [R and v= find a and b such that au + bv [:] 3

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Q: Evaluate (2z + z – i) dz J|z-il=1

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: [2 1] Q2) Assume A = |1 3 L3 4] [2 4 6 4] ㅋ 4 and B = 13 show that (AB)' = B' A'

A: Solution: The objective is to show that the given relation

Q: and B =

A: (2/5,1/5,1/2)

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: Prove that f-(U B: -U(B.), %3D i=1 i=1 and n N (B.). 3=D1 i=1

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Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: Q.Show that λ=a+d/2

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Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: 3. V4- (x – 3)²dx.

A:

Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: H.W 2: Use Cayley-Hamilton to find 4 B'and B -1 * . Where B = [12 – 101 – 13 – 1 1]

A: To use cayley-Hamilton we find characteristic polynomial. And we know that by Cayley-Hamilton…

Q: Prove (A N (B U C) = Ā U (B U C) %3D

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Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

A:

Q: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

A:

Q: 6-9 d x.dy 2.

A: A double integral is given. We need to evaluate the double integral.

Q: Let I = S (8x + 10y + 4+ 12xy) dA where R = [0, 1] × [1,2]. R Find I

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Q: Let y = 7 and U-span(u), with u = x1 = x2 = -21 TT -4. Write y=x1 + x2, where x1 in U and x2 in U+.…

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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Q: Find ([0, 2] n (1,5) – {2}

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Q: .If a v x = b v x and a v x' = b v x', then prove that a = b.

A: boolean

Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: e?dx o V1 +x

A: Prove that ∫0∞e-x/21+x2dx<(π2)1/2 Here we use Holde's inequality for two measurable functions.

Q: Find the LCM. 1) 4xy, 2x'y 2 3

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Q: E. Let 2-(e-e(3). Shn that Zy-4(xe ye")=2.

A: