Let A, Be Mnxn (F). (a) Prove that if A~ B, then At ~ Bt.

Q: Find the alue of C that satisfied the theorem for the function fCx) = 3+ Jc on the %3D in terval…

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Q: Let X N(u, 1) of size n. Obtain UMVUE for u.

A: Given that  Let X  N(μ,1) of size n. Obtain UMVUE for μ

Q: Prove that det(kA) = kn det(A) for any A ϵ Mnxn(F ).

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Q: Show that work performed by a constant force field F over any path C from P to Q is equal to F - PÓ.

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: (b) En=1 m

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Q: In Question, compute the indicated quantity using the specified inner product.

A: Given: a0+a1x+a2x2,b0+b1x+b2x2=a0b0+a1b1+a2b2 Using the identity v=v,v. 1+x+x2=1+x+x2,1+x+x2…

Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: I show that A= Hermitian

A: As per bartleby guidelines, for more than one question, only 1st one is to be answered. Please…

Q: Prove that fdr = [[ dS×Vf %3D

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Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

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Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let Myn2 defined by TCA) =A+A". Fünd bases for Ker GT) and Range CT).

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Q: Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F. dr <…

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Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: defined BCX,x). a norm Dn

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Q: y Verify Euler's theorem for u = x' In

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Q: Show that I¿(f) = 1, and conclude that f is integrable on

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Q: find the values of c that satisfy Rolle's Theorem

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Q: Suppose that h is integrable and that , h(r) dr = 0 and ſ, h(r) dr = 6. What is h(r) dr ?

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Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

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Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t&gt;0=0, t&lt;0 Therefore,…

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: 2- Prove that: Jzt=27 dz %3D 2in. Whot is the princinle nart for f(z) = ze %3D

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Define the det product ICl=C_ d s à and B, which ane glven as A=An T'+ Ay+ Az and B Bx?+ By BzP in…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: Suppose that f: [a, b] → R and g: [c, d] → [a, b] are both monotone. Prove tha (ƒ ○ g) is Riemann…

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Q: Let X,y EIR. Prove that if 21 x +35 y = 45 then x and y are not both integes.

A: Given: Let x,y∈ℝ. To prove: If 21x+35y=45, then x and y are not both integers.

Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

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Q: ) Prove that sac"()/T sec

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Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: omplete his praol of Theoren 1. B Cive ZA and ZB with AĎ || BẺ; AČ || BĚ. F D Prove: ZA is…

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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: prove that tr(aA+bB)=atr(A)+btr(B)for any A,B belongs to Mmxn(F)

A: Let A=aij and traceA=trA=∑i=1maii.. Note that, aA+bB=aaij+bbij. Then,…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: dy is then da In a If y = cosh r

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Q: show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

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Q: Let 1 an(r) : u(reie)e ino de %3D Prove that:

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Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

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Q: Let A e Mnxn(F) be upper triangular. Prove that det(A) is the product of the diagonal entries.

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Q: (a) Prove that x, y = -1, y = 1 1 (b) Prove tha and n: m and

A: This is a problem of Number Theory.

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

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Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: Prove,J w' Sin wx du %3D COSZ 2

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Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.