[1 If 3 li -2 2 31 5), find trace (A). 2

Q: Given: Z1 = 22 АВ ВЕ Prove: АС CD A

A: Definition used -            Vertically opposite angles are equal in measure.             AA…

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: 7. Show that if A and B are similar, then det A = det B. %3D

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Q: * If Iz| = Re(z), then z is

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Q: 3 2 If A = use the Cayley-Hamilton theorem to determine A?. 5 1

A: We can solve this by using given information

Q: Compute the following. |25х11+28х3 - 3х*-13х +4 dx

A: We need to evaluate the following integral  ∫25x11+28x3-3x4-13x+4dx Formula used : ∫xndx =…

Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

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Q: Part 1 of 5 (a) When a = 0.10 and n= 22, Xieft 11.591 = 32.671 Kright Part: 1/5 Part 2 of 5 (b) When…

A: a)GIvenα=0.10n=22

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: Show that D13 is isomorphic to Inn(D13).

A: Given the Dihedral group D13. We have to check this group is isomorphic to Inn(D13).

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

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Q: Which of the following correctly des -1 1 It does not exist.

A: Answer- (-1)

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: If OE = OF, then AB 2 CD. %3D

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Q: but not こ *6A-エ none of thesce

A: Let us assume two matrices A and B. To prove or disprove if AB=I then BA=I. Let us consider matrices…

Q: Is it true that if a, < b, for all nE N and E-1 a, is divergent, then E-1 bn is divergent? If false…

A: Given: an≤bn for all n∈ℕ To check that if ∑n=1∞an is divergent then ∑n=1∞bn is divergent

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: Show that if β^1 is conditionally unbiased, then it is unbiased; that is, showthat if E(β^1|X1, . .…

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Q: Let gt): csc (U) for Oct C! and CSC 2- 13/2- 2 How do I find fogle)

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Q: 32y- 154-25x= o 152 =120 2と72 3 23 3. 23 3.130437783 %3D 120 55 23 ニ 23 Y-5.217 391304

A: Solve simultaneous  linear equation

Q: Prove the following. 2. If alc and a+ b = c, then alb.

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Q: Suppose a e Z. If a² is not divisible by 4, then a is odd.

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Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

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Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: Show that U(14) = &lt;3&gt; = &lt;5&gt;. [Hence, U(14) is cyclic.] Is U(14) = &lt;11&gt;?

A: To show that the group U(14) is generated by 3 as well as by 5. Is 11 a generator of U(14)?

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: In ALMN, LN is extended through point N to point O, m/NLM = (x – 4)°, mZMNO = (4x – 17)°, and m/LMN…

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Q: 8. Prove the following (I +CD)-\C = C(I+ DC)-1 by expressing the C + CDO in two forms. i

A: To prove the below equation by expressing C+CDC in two forms. 1+CD−1C=C1+DC−1

Q: 6.4 # 2 Find the matia * ' elative to the basir B' for T A' =

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Q: ni = 22, î1 = 99.2, ô1 = 4.5 n2 = 35, îz = 82.6, ô2 = 4 Using the information above, compute the…

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Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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Q: HW KLX) = 2x+5 7 -1. Find ke-²¹ (x) 2. Prove by kok orklok

A: Let's find inverse function.

Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

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Q: If t,= 4n+1, find t,, t,, t3, and t Express t n+1, in its simplest form. n+1 In-1

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Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: For any n e N, let Bn = (n, ∞0). {B„}1 is descending. Show that Bn = 4. %3D n=1

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Q: (a) Ha: B1 0, with n = 26 andt=1.91 <p< 1 (b) Ha: B1 # 0, with n = 12, b1 = 0.16, and sp1 = 0.06 %3D…

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Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

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Q: If det A= 0 why is det A+ = O? If A has rank r, why does A+ have rank r?

A: Given Data det A=0   Suppose the column and row of the matrix are linearly independent. The matrix…

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: prove the following:

A: Given,           f(x-y, x+y)=2(x2+y2) To prove that,          ∂f(x, y)∂x+∂f(x, y)∂y=2(x+y)

Q: 1 2 1 -Given that B= 1 -1 0 3 1 1 Show that B,-B,- 6B = 1. Hence, deduce that B' = B² -- B – 61.

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Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Show that yn Z, if n³+5 is odd then n is even

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Q: (c) If gcd(a , 133) = gcd(b , 133) = 1, show that 133|al8 b18 %3D %3D

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