3. Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel. 3x + 2y - z = -2.1 -4x + y + 7z = 26.2 2x -4y+ z 4.2 Ans.x = 0.5, y = 0.2,z = 4

Q: Show that the equations x+ y +z = 4, 2x + 5y - 2z = 3, x + 7y - 7z = 5 are not consistent.

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Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: The general solution for the Euler DE x2 +2xv -2y%3D0,x>0, is given by O b.y= Gx=2+ C2X. O d. y=…

A: The general solution to the Euler DE  is , where, are the roots of the equation, .

Q: . Apply Gauss-Jordan method to solve the equations x +y +z = 9; 2x - 3y +4z = 13 ; 3x + 4y +5z = 40.…

A: given , equations  x +y + z = 9 2x -3y + 4z = 13 3x + 4y  +5z = 40  apply gauss jordan method

Q: Is (2, –1, 3) a solution of 3x + 5y – 2z = -5 2х + Зу- z 3D —2 2x + 4y + 6z 18? Replace x with 2, y…

A: Consider the system of equations. 3x+5y-2z=-52x+3y-z=-22x+4y+6z=18 And, the solution of the system…

Q: Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel.…

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: This is the solution of the Cauchy - Euler equation x²y" + 17xy' + 60y = 0 O y = C1x 5 + C2x 8 O y =…

A: Using method of Cauchy's Euler Equation

Q: (10) Use the result of Exercise 9 to find the geeral solution of the given equation: (a) (r-3)?y" +…

A: Please see the explanation below

Q: In ARST, mZR = 47°, m 2S = 3y - 7, and mT = 2(y + 10). Find the value of y. %3D %3D %3!

A:

Q: A second order Caushy – Euler equation having a solution y(x) = x-2cos(4Inx) is x?y" + 5xy' = 0 O…

A:

Q: Prove that y = C,x² + C2x²lnx is a solution of the different equation x2y" – 3xy' + 4y = 0 and then…

A:

Q: 5. Determine a solution of the following equation which satisfies the given condition: y-3y'+ 2y = 0…

A: Given that, The differential equation is following, y''' - 3y' + 2y = 0 y(0) = 0,  y'(0) = 2  and…

Q: (*) Solve the following equations using the method of characteristics. In each case, if the Cauchy…

A: By Bartleby policy I have to solve only first one as these are all unrelated & lengthy…

Q: 5) a) Construct the equation Aª A£ = A™ b_ in which its solution gives the best line = (C, D)for m…

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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: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

A:

Q: Find the solution of the Euler-Cauchy equation x²y" + 0.6xy' + 16.04y = 0.

A:

Q: For what values of the parameter A, will the following equations fail to have unique solution: 3x -…

A: Given equations are 3x−y+λz=12x+y+z=2x+2y−λz=−1 Write it into augmented matrix form, which is given…

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: a*y, u (a, х, 2х + 2 Uz + xUy = x²y, 5x

A:

Q: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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Q: y(4) + 3y" + 2Y = 0

A:

Q: Find the solution for the equations using Gauss-Jordan. Then ONLY give the answer for x+ y+x…

A: Given: x+y+2z=92x+4y−3z=13x+6y−5z=0

Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

A:

Q: (a) Verify that yp, = 3e2* and y,, =x² + 3x are, respectively, particular solutions of y" – 6y' + 5y…

A: To verify the given statement and to find particular solutions by using the given statement.

Q: Based on the following: i: x ≥0 ii: y ≥0 iii: z ≥0 iv: 0.5x + y + 0.2x ≥ 600 v: 2.0x + 3y + z ≤ 2000…

A: Here we have to solve y+0.2z = 600 and 3y+z = 2000 and find the values of y and z. Before that let…

Q: Solve the following Cauchy problem: -00 0, u(r,0) =r-r, (x,0) 4r, -x <r<x.

A:

Q: Find an actual explicit solution to y'=t/y,y(2)=- O y(t) = -(t^2 - 3)^1/2 O y(t) = -(t^2 - 3) O y(t)…

A: Given query is to find the solution for the differential equation.

Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

A:

Q: b) Show that if y(t) is a solution of the problem y" +e*y + y = 0, y(0) = 1, y'(0) = 2, %3D then…

A: Given y''+e-ty'+y=0, y0=0, y'0=2

Q: Solve the equation Ax = b by using the LU factorization given for A. 4 - 4 4 1 0 0 4 -4 4 - 4 A = -…

A:

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: = 2 y" + y = 0, y'(0) = 0, y' () 2 ||

A: We have to find the particular solution of the given boundary value problem   y''+y=0,  y'(0)=0,…

Q: (b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

A:

Q: 1. Find the number of non negative solutions to x + y + z + w 16. With the conditions that x > 2, y…

A: The complete solutions are given below

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: Identify the Cauchy-Euler equation. O g- 52* + 8y = 0 dz4 22 y" – 7xy' + 6y = 0 O 2y" + 2a?y" – y' +…

A:

Q: Let d = gcd(a, b). If (xo, yo) is a solution of the linear Diophantince equation ax + by = c, %3D…

A: It is given that d=gcda,b, x0,y0 is a solution of linear Diophantince equation ax+by=c.

Q: B. Prove that the given equation is a solution to the given DE: 7. y = Ax + Be* ; (x- 1) y" - xy' +…

A:

Q: 1. Determine the values of the variables to satisfy the equation using Jacobi. 5a - 2b = 40 Ans. a =…

A:

Q: The solution for the IVP: -00 %3D u(x, 0) = 2 x u(x, 0) = -e-x O a u(x, t) =x+ -(x+21)-e-(x-20) 4 O…

A: Known fact: For the system, utt=c2 uxx,   -∞&lt;x&lt;∞, t&gt;0ux, 0=fxutx, 0=gx The D-Alembert's…

Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: Suppose that r, y, z satisfy the equations x+y+z = 5-a %3D 2x +y = 7 – a %3D x - y – 2z = 0, %3D…

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Q: Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel.…

A:

Q: Eliminating the parameter from x = f(t) and y = g(t) means eliminating_______ from the pair of…

A: In parametric equations are the quantities are represented by the functions of a single independent…

Q: 3x?y" + 2xy' = 05 21"

A: Differential equation

Q: A third-order Euler equation is one of the form ax°y"' + bx-y" + cxy' + ky = 0, where a, b, c, and k…

A: Givenax3y"' +bx2y" +cxy' +ky=0 ----1after subsitution V =lnx Transformed into constant coefficient a…

Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Q: A second order Caushy - Euler equation having a solution y(x) = x=²cos(3Inx) is Ox²y" +5xy' + 4y = 0…

A: