Example 6.13. Prove that (1) A = & + , I + 4

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: 10 Prove that: ²x = 1 (g)(x) m = 1 so that the product

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Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

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Q: (a) Show that xn → x and Yn →y implies Xn + Yn → x + y and also show that an -→ a and Xn → ax. → x…

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Q: 1. Prove that 1 {2" : n E Z} = {; :n e Z}. 2n

A: I used the fact that two sets are equal iff they are subsets of each other

Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

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Q: 1) Let 1 = f²f²e-³x-2y dydx. Then / = e-12-26-41 b. +2e-*- 3 d. None of the above

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Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: 31. Prove parts (a), (c), and (d) of Theorem 3.1.1.

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Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

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Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: Solve this problem About Faktorial with the full step, thank u Prove that :…

A: Note: There seems to be a typo in the question k!(k−2)!(k−1)!(k−3)! and the actual question should…

Q: 10 3. Prove that the L{10e2} = s-2

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Q: z = ecos(2x)

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Q: 2. Find the inverse of A = == CN 2 1 -1 3 - -1 2 2 22 12 3 2 using Gauss-Jordan method.

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Q: n2 1 SHOW ALL OF YOUR WORK. 3. an = 2n +1 2n + 1" (а) Find aj, а2, аз, а4. 3 (b) Compute > a;. i=1 4…

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Q: Use Heaviside Expansion Theorem (2s^2+1)/[(s-2)(s^2-2s+5)^2]

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Q: 5 0.6 0.1 Apply Gershgorin's theorem on B = -1 6. -0.1 1 2

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Q: -4 -2 Let E= 0 Find 2E. -3 5

A: Given,  E=-4-204-35

Q: (2, 1) entry of A – B" equals 0. Is ~ reflexive? Is ~ symmetric? Give a brief justification for your…

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Q: 4) We know that () and a!=1.2...a. Prove that Yn75, )< 2n-2. G0od Luck!

A: Given, ab=a!(a-b)!b! and a!=1.2....a

Q: 7. (a) Find all the values of z such that e = 1+ i.

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Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: 2.3.12 Prove Lemma 2.3.10 (2). Only need to prove #2 0f Lemma 2.3.10. Lemma 2.3.10. Let a E R. 1. a…

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Q: 23 1 dr Evaluate - Express your answers in the form: Axm + Br" + DxP.

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Q: Calculate the residue of eZ.e-5=0

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Q: 34. Prove parts (a) and (c) of Theorem 3.2.3.

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Q: -1 7 24 41-69 - [ ³ 4] = -2 9 B 07 02 00.0 ↓ 1 e dimension of the result. (If not possible, enter…

A: Topic:- matrix algebra

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: 2 -1 2 3 0 1 5 1 -2 03 -2 -4 1 6 7. Check your answer in item 6 using Cofactor expansion. 1

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Q: homogenous DE 3udv-vdv-udu-vdu=0

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Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (c) Use part (b) to show that Fn-1 00 00 (-1)"+1 - Fn Fn+1 n=1 Fn+1 n=1

A: Consider the given information: The part (b) states that  -1n+1=Fn2-Fn+1Fn-1 To show that,…

Q: 10:29 ll LTE O True or False 11. If two figures are congruent there is always just one way to…

A: Statement is given  We have to define it is true or not

Q: 1.5 Prove that |e=2=| 0.

A: We need to prove that |e-2z|&lt;1 if and only if Re(z)&gt;0 The solution is detailed below.

Q: 3 (5) Suppose that T : R³ → R² „such that 2 1 1 T (e,) = T(e.) T(e,) = and T (e,) = 1 1 3 2 T Find -…

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Q: 2 In x 1 e* 2 1 In 2x -1

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Q: 71 Compute Σ (5k2 + k - 3) i=1

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Q: Example:3 Verify Cayley-Hamilton theorem, and find A-1 [2 1 1 A=0 1 l1 1 2.

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Q: Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an…

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Q: Example:4 Verify Cayley-Hamilton theorem. Hence find 2 -1 A-1, A -1 2 -1 1 -1 2

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Q: Transform of the followi 2. + (5) = 35-25-1 (S-3) (5²+1)

A: Given that  F(s)=(3s^2-2s-1)/((s-3)(s^2+1)) To find the inverse laplace of F(s)

Q: 14. Substituting appropriate values for x and y into the formula of Theorem 9, show that (a) = 2";…

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Q: re + e Show that 1. 2

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Q: Q.No.6. Prove that by mathematically Induction 2" 2.

A: Let Pn: 2n&lt;n+1! For n=2 LHS is 22=4 and RHS is 2+1!=3!=6 As 4&lt;6 So, Pn is true for n=2 Let the…

Q: 6. Inductively prove that B(0) = 0 for all n. Conclude that B(2) is C° function. %3D a

A: We prove the above theorem by induction. We have to prove that Bn0=0 ,∀n...1 Take n=0 then, Bn0=B0=0…

Q: 13. a) Show that EX=o (-1)*(")=0, and then verify that ) +C) + C) + - - G) +G) + () +- ... = b)…

A: We will use of binomial theorem to solve it

Q: 1. Let A = and B = For what values of t is 2A +B invertible?

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