Using LU Decomposition Method, determine the roots of the following equation. Explain how the answer was derived    4w +1y+1z=2 3w+1x+3y+1z=4 1x + 2y = 6 3w +2x+4y+z=8

Q: Under what conditions is yb+6c perpendicular to a? What does this say about the coefficients of b…

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Q: From the given equation below, compute x1, x2, x3 using LU decomposition. 2x1-3x2+x3=15…

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Q: B) Use the LU decomposition you found earlier to 6 Txl 3 1 -6 0 -16 x2 =| 4 8 -17x3 17 solve

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Q: 7 dx 5. S 3 xVx-4 2

A: dsec(u)du=tan(u) sec(u) ∫cos(u) du = sin(u)

Q: Solve the equation Ax = b by using the LU factorization given for A. - 6 4 0 0 4 -6 4 6 A = - 12 16…

A: Ans _ A=4−64−1216−78−104=100−3102−114−640−25001 and b=6−82Let l y = b100−3102−11y1y2y3=6−82y1=6 —…

Q: SHOW YOUR DETAILED SOLUTION Find an LU decomposition of: 2x+5y=16 3x+y=11

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Q: -3z (D² + 6D + 9) y 16e x²+1

A: Left hand side quadric equation will be use for solving or extracting the roots. Which will give…

Q: Find the roots of the linear equations using Crout's Method. 5X1 + 4X2 + X3 = 3.4 10X1 + 9X2 + 4X3…

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Q: Solve the following using LU decomposition: 2a + 5b+ 4c + d = 20 1.) a+3b+ 2c+d =11 2a +10b +9c+ 7d…

A: Total Equations are 42a+5b+4c+d=20→(1)a+3b+2c+d=11→(2)2a+10b+9c+7d=40→(3)3a+8b+9c+2d=37→(4)Now…

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: Use separation of variables to find a product solution to the following: д н ди -u=1.k>0 дх2 дг

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Q: obtain a formula for the local truncation error for the Euler method in terms of t and the exact…

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Q: Find the two conditions on b1, b2, and bz which determine solvability of 4 8. 3 4 =6= b2 -6 -7 -8 b3

A: The objective is to form the equation involving b1, b2, and b3 that determine the solvability of the…

Q: Find the second approximation to the root of the equation x-4x-9 = 0using bisection method, if a, =…

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Q: (b) Solve the following IE u(x) = f* (z + 1²) dz by "Adomian Decomposition" method.

A: Solution:

Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A.…

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Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: Use the Disk Method Y= x^(3/2) , Y = (3/2)x , revolved around X = 5

A: First we have to design the integral using the given conditions,  and for that obtain functions of…

Q: Exercise 1. Find 뿐 for y =DIn (골) (1A) + 3극 3z-2 z(r-1) (1B) 분 (1C) -= (1D) 를-3금 z-1-r z(1-1) (1E)…

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Q: quadratic form 1.) 2xy+6xz-4yz 2.)x2+y2+z2+2xy

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Q: 12 Consider the DE: x' x, with solutions x = est [3e L4e-2t and x, = a) Verify that x, and x2 are…

A: By finding the wronskian of the solutions

Q: Solve the equation Ax=b by using the LU factorization given for A. 2 -5 2 2 -5 2 8 -6 12 - 1 -3 10 O…

A: Given,A=2−52−612−14−70LU factorization of A is−A=LU=100−3102−112−520−35001b = 8-124Let, x = x1x2x3…

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: Find the general solution of the given differiental equation using the undetermined coefficients…

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Q: find the engle of intersection between 2x - 4y + 4z = 7 and 6x + 2y – 3z = 2 .

A: Consider the given planes: 2x-4y+4z=7So,n1→=2,-4,46x+2y-3z=2So,n2→=6,2,-3

Q: Write down all of the product solutions satisfying: и +иу —D 0, 0 <x<2, 0<у<1. %3D u(х,0) — 0, и,…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Q No. 1: Solve by using Adomian Decomposition Method d?v dv +r· dr2 (n²n²r2 2A ==(Pr+1), r2. - dr d2…

A: Adomian Decomposition Method is used to solve the differential equations for both ordinary and…

Q: > -3X1 + 9X2 + X3 = 6 • 5X1 – 4X2 + 15X3 = 9 • 4X1 – X2 + 2X3 = 15

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Q: Make a change of variable, x= Py, that transforms the given quadratic form into a quadratic form…

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Q: Solve the following linear equations using Crout's LU decomposition method. 2X₁5X2 + X3 = 12 -X₁ +…

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Q: 1. Find the roots of the linear equations using Crout's Method  5X1 + 4X2 + X3  = 3.4 10X1 + 9X2 +…

A: given system of equation 5x1+4x2+x3=3.410x1+9x2+4x3=8.810x1+13x2+15x3=19.2 use crout's method to…

Q: Solve using the bisection method f(x) = e-x* – 2x + 1 starting at the interval [0.75,1]

A: Consider the provided question, We have to solve the given function by using the bisection method,

Q: Consider AB in the coordinate plane below. 10 4. 2. A -10-9 -8-7 l0 1 -1 -5-4-3 -2-1 2. 4. 10 -2 -3…

A: Given: AB¯

Q: find the genral solution (D +2D,D, -2D, +2)u = 0

A: Given  Dx2+2DxDy-2Dy+2u=0   …………………(1) Consider the equation F(Dx,Dy)u=0 Here F(Dx,Dy) =…

Q: Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form…

A: Let the Quadratic form for the given expression is Q(x)=xTA x=7x12+6x22+5x32-4x1x2+4x2x3 , where…

Q: Solve

A: We solve by Cholesky Decomposition Method.

Q: Find the cross product á xb and verify that it is orthogonal to both á and b for á = i+ 33 – 2k and…

A: Given:-a→=i→+3j→-2k→b→=-i→+5k→To find: cross product a→×b→

Q: From the given equation below, compute x1X2, and X3 using LU decomposition. X1 — 3x2 + Xз 15 ЗX1 +…

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Q: From the given equation below, compute x1X2, and x3 using LU decomposition. X1 — Зx2 + Xз %3D15 3x1…

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: Q6) Use LU Decomposition method to solve the sy stem: 6x - y - 4z = 9.3 x + y – 3z = 1.9 x + 2y – z…

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Q: 5t 2 ; Consider the DE: x' = x, with solutions x, = 1 [3e* and x2 = 12. - L4e-2t] a) Verify that x,…

A: See the detailed solution below.

Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

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Q: Find the root/s using Bisection method a) x2 - 6x + 9 = 0 b) x - e-* = 0 c) f(x) Ans. x = 3 %3D Ans.…

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Q: ind the roots of the linear equations using Crout's Method 5X1 + 4X2 + X3 = 3.4 10X1 + 9X2 +…

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Q: Q6) Use LU Decomposition method to solve the sy stem: бх — у — 4z 3D 9.3 у — 42 x + y – 3z = 1.9 x +…

A: for a linear matrix AX+b, if a can be written as LU matrix, this means we can rewrite Ax=b as: Ax=b…

Q: Make a change of variable, x =Py, that transforms the given quadratic form into a quadratic form…

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Q: Classify each of the equations below as separable, linear, solvable by a standard substitution (i.e.…

A: Important instruction: According to the Bartleby guidelines, only the first three subparts of a…

Q: Find the roots of the following set of linear equation using Doolitle's Method X, + X2 + X3 = 5 X, +…

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