Determine the LU decomposition (without pivoting) of the following: 2 2 1 - 2 1 4 91 00 8 O 1 0 0 L= - 1 1 0 -4 1/13 1 1 L= 1 1 0 0 L= 1 1 0 4 - 1/3 1 L= 1 -4 -1/3 1 1 0 0 1 4 1/3 1 0 22 1 U= 0 3 5 0 0 14/13 22 1 U= 0 3 0 0 14/3 22 1 U= 0 3 5/3 0 0 14/3 22 U= 0 3 5 In 0 0 -14/3

Q: a) Determine the formula for the Laplace transform. L{6e^-3t-t^2+2t-4} (type an expression using s…

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Q: Q1. x= [5, -3, –1, 2]" is a 4-dimensional vector. Calculate the following values: 1. the squared…

A: Given 4-D vector: x=[5,-3,-1,2]T We have to find the Norms of the vector. Norm is the magnitude of…

Q: 1 2 3 2 4 7 1. Let A = 3 6 10 3 6 10 (a) Find an LU decomposition of A. 1 (b) Use the LU…

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Q: ft) = cos 2t + sin 2t + cosh 2t + sinh 2t 2s? (s+2) А. (s2 +4)(s2 -4) 2s? (s-2) С. (s2 +4)(s2 -4)…

A: We find the Laplace Transform of  f(t)=cos(2t)+sin(2t)+cosh(2t)+sinh(2t).

Q: Find the Laplace Transform of the following: 4) e3z-2bt  (variables other than t are considered…

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Q: Let y = - 11 - 1 1 9 1 0 - 1 2 , and V₂ = -6 1 . Find the distance from y to the subspace W of R4…

A: y =

Q: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

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Q: Ry (@)= [ cos 0 Rx (@)=||0 o coso -sin@ sine Cose o sind Kz(4)= | cost - sint o Siny cos 4 O -shd o…

A: Given that, Rx(θ)=1000cosθ-sinθ0sinθcosθ, Ry(ϕ)=cosϕ0sinϕ010-sinϕ0cosϕ, Rz(ψ)=cosψ-sinψ0sinψcosψ0001…

Q: Use the Gram-Schmidt process to transform the following sequence of vectors into an orthonormal…

A: Given vectors are  and .We have to transform the following sequence of vectors into orthonormal…

Q: Perform the Gram-Schmidt process (with normalization) on the following sequence of vectors. 18…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: 7. 26-² s(s² + 4s +13)

A: We have to find the inverse Laplace transform of Lets use partial fraction decomposition first.

Q: y = (−3, −2, −1, 5) and 4 5 2 1 3 0 3 2 2. 1 A= 2 -1 * REQUIRED 18. Compute the resulting vector of…

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Q: Use Laplace Transform to solve each of the following IVPSS a. y" - 2y' + 2y = 0; y(0) = 0, y'(0) = 1…

A: We will use the laplace transform on both sides of given equation to obtain Y(s) then after that we…

Q: 4 None of the Choices f(t) 1 (e²+ e ²¹)-(e₁-e²₁) Option 3

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Q: 1. Find the Laplace transforms of the following by the method indicated showing details of your…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: (a) Compute the dot product of u = (b) Compute the magnitudes of u and v. (c) What can you say about…

A: Given two vectors u and v, we have to find a) Dot products of u and v.  b) Magnitudes of u and v.…

Q: 1. Find the closest point to y in the subspace W spanned by u₁ and U₂. y = -1 3 , U₁ = 1 1 0 U2 -1 0

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Q: 3 2t Find the laplace transform of ett²+ e²t (2cos 3t). - 16

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: Calculate the 2D-DFT of the following image. 10 0 1 Table 1: A Digital Image.

A: Solution: Given that N=2 fx,y y=0 y=1 x=0 1 0 x=1 0 1 Now,

Q: 1. Solve the following difference equation by using Z-transform by replacing the value of M as per…

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Q: 1. Find a basis for the orthogonal Conplement of the Subs pace of IR? Spanned by the vectors…

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Q: A) Find the Laplace transform of the following:- 3) L(Vi +e-t)* 4) L(e2 cosh 3t - e t5)

A: Laplace Transform: Given a function defined for all real , the Laplace transform of is a function of…

Q: Find the Laplace transform of the following: a.) f(t) = -13sin(-18t). If s = -4.86, what is F(s)?…

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Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s2-12s-8] L-1 1)…

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Q: f(t) = sinh? 4t cosh 4t 32s А. (s2-144)(s2-16) C. 4(s2 -144)(s2 -16) s3-4s? +560 В. (s2-144)(s2-16)…

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Q: s+1 (a)x= ¹ {= 1/12) b)x=² { = s²-4s Q1) Find: a)¯¹) 3s + 1 s²-4s+1)

A: We know  and

Q: (c) Write C(A) as the span of a set of linearly independent vectors. (d) Write N(A) as the span of a…

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Q: 3 s² + 6s + 13

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Q: Please show all working out preferably handwritten

A: Step 1:Step 2:Step 3:Step 4:

Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find  The vector closest to you from the subspace of R^4 spanned by v1 and v2.

Q: Solve by the Laplace transform, showing the details and graphing the solution: 1. y" – y' – 2y = 12u…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 6.1 Which of the following functions, depending on the variable s, does NOT have a continuous…

A: 3rd one is C

Q: 3. Which of the following is the Laplace transform of sin (2t) - 2tcos (2t) ? A. s^2 / (s^2 + 4) ^2…

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Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr