7) Calculate the Method s Syluester and prorection motrix CP method) for the function Hi diagonali2ation using cayey 3 different Hamilton- which are -21 Cuse all three methods.)

Q: by computing that the given funetions inde pendent on Show the are linearly indieated intorvale…

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Q: 2. Using OLS or any other suitable method, Prove that E(ß1) = B1 E(ßo) = Bo

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Q: b. In Z6(x], let f = 2 + x + 4x² + 3x³ and g = 4 + 3x+ 5x² + 3x³. Compute f + g and f.g and their…

A: In the finite field we only use the coefficients from that field . The degree of polynomial is not…

Q: Find Tay br Polynomial. for the function fox): Vx + 3. ot degree 3 centered ata=2

A: According to the problem, we have

Q: How many invertible functions exist with the signature Za→ Zb if a = b? %3D

A: To find the number of invertible functions from ℤa to ℤb. Given that a=b. Also ℤa has a elements.…

Q: Use the tabular method to to prove the following in general 1. (ANB) C (AUB) 2. ΑΔΒ = ΒΔΑ.

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Q: Prove that the effective factor is a Hermitian factor in a specif and x-i

A: Momentum operator is defined as an Hermitian generation of translations, then it is hermitian by…

Q: Are there any nonconstant polynomials in Z[x] that have multiplicativeinverses? Explain your answer

A: No, there is no any nonconstant polynomial in Z[x] that have multiplicative inverse.

Q: Construct the Lagrange Interpolation polynomial for the fundlion y= Sinin taking the points. 6.

A: Given  y=sin(πx)x0=0,x1=1/6,x2=1/2

Q: Find the value of the Sallowing Polynomial at all x Ualue s in the in terval Lo, 3 Use step=al

A: Here we know x values range from 0 to 3. So we need to find the value of polynomial P at all x…

Q: In Z3×U3, Find the order of (1, 2). Show your work.

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Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: Let A Find grad(div( A ) %3D

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Q: Find the and the sroallart Valurs of the functron fx)%=Ie+t on The intosval 0< ILI %3D

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Q: prove that div A マ - Kr

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Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: The number of reducible monic polynomials of degree 2 over Zz is

A: The number of reducible monic polynomials of degree 2 over Z3 is

Q: Find the rank of A= = xS+ x + invertible. [exham S] O A MOITERUD 225 10-4 and explain why it indic 4…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Save the following Sef of Lincay equations using over relaxoation 10X, +X2 + X3 12 X, + 10X2 + X3 =…

A: Rewrite the given system of equations, to find x1, x2 and x3. Multiply each right hand side…

Q: i) Find an upper bound for the modulus 3z³ + 5z + 1, if |z|<1 where z is the complex number.

A: Now for the mod function: : a+b≤a+b. SO using the same method in the given complex function:…

Q: 1. Write the finite difference approximation of u – uxx = 0 in the explicit method used to solve…

A: The complete solutions are hoben below.

Q: (a) through the midpoint rectangular rule and (b) through the trapezoid rule. Discuss your results…

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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: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: Calculate x - z. (Image 24 JI 8х -2 2x +1 3z z + 22

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: 3) Find the mZT= %3D

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Q: 2 1 Find a mat rix P such that P- 2 0 0 3 0 3 [11 O AP = 1 0 -1 0] BP = 1 1 1 1 OCP = 0 1 1 -1 ODP =…

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Q: By using Ho(x)=1 and Hi (X)=2x in Hermit Polynomials, caleulate the Valne of Hg L)? (1)

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Q: 5. Use De Moivre's Theorem to evaluate (1 – V3i)%.

A: Demoivre's Theorem

Q: such that ab = 1 b) : In Z3XU3, Find the order of (1, 2). Show your work.

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Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

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Q: Is there a km. lenRit 3 Why 3 kM. X4-2x If there is a konft prove 9t by using the (E-8) defnti9on of…

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: 6) let fl2) = CosCitaiy) 22atey Express flz) that f satisfies in the form and fornd z So the Canchy-…

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Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: 5) Find oll volues of + that moke A invertible A= 211 31t

A: The detailed solution is as follows below:

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

A: Let,

Q: Use Eisenstein Criterion to verify that , If p = 2, f(x) = x² – 2 is irreducible %3D over Q. State…

A: Explanation of the solution is given below...

Q: Determine all the number(s) c which satisfy the conclusion of Rolles Theorem for

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Q: -3 [-1+v3i]

A: Explanation of the answer is as follows

Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: Find a method that can produce infinitely many triples (a, b, c) with no common factors such that a…

A: To find - Find a method that can produce infinitely many triples (a, b, c) with no common factors…

Q: Given two polynomials in from of x^3+x^2+x+c =0 x^3+x^2+x+c =0

A: Given: To find their intersection using matrices. Given two polynomials in from of…

Q: How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with…

A: Set of all Polynomials over a field ℤ7 is given by ℤ7x=anxn+an-1xn-1+ . . . +a1x+a0  where a0,a1, .…

Q: consider fixi) = %3D show that trany2 eloes net suhsty kipschifzconchition elo muiswechenclndes ino…

A: 3

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: Find the polynomianl degree 9 centered at 0 that best approxixmates f(x)= f(x)=1/ 7sqrt(1+x^3) Now…

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Q: 3. Prove that the sandwitch theorem.

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Q: Use the error bound for SN to obtain another proof that Simpson’s Rule is exact for all cubic…

A: