4. Prove the statement of 3 on page 9 of lecture notes 10, i.e., SSE xa-1)(0–1)*

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: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

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

A:

Q: 9b of sido s8 Into4 gnggit EGcops otivostnsliM If ((h IR>R such that h(x) =x-6) and (g R --63-70000R…

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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: Vhich among thế chôičes satist etters only. 2а. у" - Зу'- 10у %3D0 Co-5x C o2x

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Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

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 the series 3. + + 4 To t (-1) Lonverges absolutely.

A:

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

A:

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

A:

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To prove the inequality regarding membership function of the symmetric differenece of two fuzzy sets

Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

A:

Q: 3. Is this sentence consistent? “There is someone who loves exactly those people who do not love…

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Q: 1 -dr. a In r| Find 3.

A: Let's find.

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: 1. Suppose that is the answer to this question. Determine the value of -

A: To determine the value of 1/x

Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

A:

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: Prove the following: 1) 1+3+5...+ (2n-1) = n²

A: *By Bartleby policy I have to solve only first one as these are all unrelated  problems.These are…

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: 1) Solve the O.DE. qiven below y'+ 3yt= tye"

A:

Q: II. Prove the following. 3. 7|23n – 1, Vn EN -

A:

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 3.1 State the Weierstrass M test theorem.

A: Note: As per our guidelines, we will solve only first question. If you want any specific question to…

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

A: Let's find inverse function.

Q: Prove that tanodo-n//2.

A:

Q: What statement could be used to prove that m tn?

A:

Q: 2+13 Evaluate zdz along the following paths- (a) horizontally from 1 +i2 to 2+ i2 then vertically to…

A:

Q: 8) Use Theorem 7.2.1 (Table) to find the following: 3 b. E s' +9s

A: We need to calculate the Laplace inverse of 3s3+9s . We will use the two formulas ,…

Q: 9 show Itat Ihe maclayvin Sevies For Hense is メ+ メ t.. 4- X

A:

Q: + .... Ex. 5. Prove that P,(-) = P,(-}) P,(4) + P,(-1)P2m -1 () + -. Pa(-)P.().

A:

Q: By 2 Cas X the Same. way prove that

A: Prove that J-12x=2πx cosx

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: 7) Show that K± = det [ T 4 J.

A: Sol

Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.