b) Find the transformahón to reach diagonal form. a

Q: Use the Fourier transform method to show that the transform solution of the (n+1)-dimensional,…

A:

Q: Find the Z transform of:

A: In this question, we used the formula for Z-transform which described in step2

Q: Show that the CAPM Bi is linearly additive. Present all your calculations analytically and explain…

A: Given Solution:

Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: 8 Use the method of Laplace transforms to solve each IVP.

A:

Q: Compute the orthogonal projection of ữ'onto 7. Use the square root symbol 'V' where needed to give…

A: Projection of u→ onto v→ is , projv→u→=u→.v→v→.v→v→

Q: Find the Hankel transform of xve-ax, taking

A:

Q: 5- Fit)= b Uct-a) -2b4lt-29) + bu(t-34) %3D Laplace transform

A: The detailed solution is as follows below:

Q: The inverse z-transform of (a) (-a)" [] 2₁] e-a-3 (z-ea)(z-3) -, a>0 ROC: ea <z<3 is,

A:

Q: Prove that a rotation of θ = π/4 will eliminate the xy-term from the equationax2 + bxy + ay2 + dx +…

A:

Q: What are the coordinales of T for the transformmation (T-3, 1) D.XATUV) of T(-7,-6), U(-8, 3), and…

A:

Q: Find the Fourier transform of f if (e* jkax > 0 * ikax<0 Note : jika = if

A:

Q: T is a linear transformation from R² into R². Show that T is invertible and find a formula for

A:

Q: 1. F, (2х — у)аА, D está acotada por el círculo con centro en el origen y radio 2

A:

Q: 3. State and explain the Convolution Theorem for Laplace transform

A: To prove: State and explain the convolution theorem for Laplace transform.

Q: Find Linear Fractional Transformation that maps the given three points onto the three given points…

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

Q: Find the Laplace transform of 6t - 5te+5. L{6t- 5te ¯' + 5} = %3D

A:

Q: Use the laplace transform method to solve the given system

A: The system is  d2xdt2+dydt-y=02dxdt-x+dzdt-z=0dxdt+3x+dydt-4y+3z=0 Apply Laplace transform:…

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

A:

Q: 4. Find the inverse z-transform of X(Z) = (22-4) (2+3) Xx and also find o, 1,

A:

Q: Solve The fallowing funcbions by using Laplace transformahions

A: Solve by using Laplace transfer

Q: 4 (1 + cosh(t))2

A: Introduction: Laplace transformation is important in the design of control systems. It is necessary…

Q: Find the fourier transform of: | coshw,t

A:

Q: I have not yet been taught Laplace Transform by my lecturer, I believe. Isn't there another way…

A:

Q: Compute the transform equation of the curve xy = 1 by rotation of axes through 45°? %3D

A:

Q: The Jacobian of the transformation x=ư - v, y= 2uv, is u + v?.

A: Given, x=u2-v2           y=2uvThe Jacobian of the transformation of x=u2-v2,…

Q: (A) Compute the discrete Fourier transform of f = 2 – 2t on [–1,3) with length 4. F{f} = |

A: (A) Consider the given equation: Length N=4 Time division is 13 Then Then, Now, So,

Q: Solve this problem with Laplace transformation:

A: In this question, we solve the wave equation by using Laplace transformation.

Q: 7. Find the canonical form of (x+y+z)². Also specify the corresponding orthogonal transforma-

A: Given expression is x+y+z2. We have to find the canonical form of x+y+z2. Expand x+y+z2, we get…

Q: Use Laplace transform to solve IVP shown below: у" — 5у' + бу %3D2tet - Зet | У (0) %3D 1, у'(0) %3…

A: Given y''-5y'+6y=2 t et-3et, y(0)=1,  y'(0)=-1   To Use Laplace Transform to solve the given IVP

Q: -et Cos wot Z a tj w 2 t Wo

A: We have to use Fourier transform formula.

Q: Find the Jacobian of the transformation x 2u, y = 2uv and sketch the reg

A: (a) Given,             x=2u, y=2uv

Q: Give 5 simple or basic examples of Laplace Transforms with solution.

A: First example: We have a formula Ltn=n!sn+1 So, one example is for n=2: Lt2=2!s2+1=2s3 Hence,…

Q: such that M2,2 into Let T be a linear transformation from M, 2 (::)-(: :) (::)-(:: (::)-[::} (::)-[:…

A:

Q: Find the Laplace transform of 4cos3t - 5sin3t.

A:

Q: Find the image of the Z-shaped figure at right with vertices (0, 0), (6, 0), (6, 6), and (0, 6)…

A: Now , we have got 4 points .  We first try to find the image of those points then plot them on the…

Q: 1- Show that: |(1 -x²]-1/2 dx = 2 VIT %3D Hint: Make the following transformation: x2 = y

A:

Q: 1 Prove that the inverse transformation W = - transforms the straight line ax + by = 0 is a straight…

A:

Q: Find the z - transform of IN k

A:

Q: 3. get) わ Fessa 2 2.

A:

Q: If a function is Fourier transformaboe, is there any guarantee that the function will be Laplace…

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Q: Solve the ODE y''+y= sinxcosx using the superposition approach

A:

Q: Determine the Laplace transform of 2et cos (6t - T). CO 8-4 3/3 (금) s2-8s+52 s2-8s+52 ㅇ (-) -85+52…

A:

Q: (i) Find the Z transform of {xk} = {3k=2 + 4k+1 +8*k}. %3D

A: To find Z transform of the sequence xk=3k−2+4k+1+8kk

Q: Find the linear fractional transformation that maps (1, 0, i) to (1, 0, 1+i).

A: The formula for transformation is given by: w-w1w-w3·w2-w3w2-w1=z-z1z2-z3z-z3z2-z1 Here, w1=1, w2=0,…

Q: 3. C-1) " Conditionally absolutely codvergent divergent. Con vergent, 2n+ Sinin) or

A: Solve the following

Q: Find the 2. transform of the tollowing Signal x(k)= %3D otherwise

A:

Q: Show that I transform fix k= 0,132g---- into TK+I Itfr, linear "diffexence equation: Yam= Jk

A:

Q: a/Find the in Verse transformL (F6)

A: