DIRECTIONS: SOLVE THE FOLLOWING SYSTEMS OF LINEAR EQUATIONS BY LU DECOMPOSITION METHOD AND BY CRAMER'S RULE 1.) 2x+5y=21,x+2y=8 2.) 2x+5y=16,3x+y=11 3.) 2x+3y-z=5,3x+2y+z=10,x-5y+3z=0 )x+y+z=3,2x-y-z=3₂x-y+z=9

Q: 2. Let a linear system of equations Ax = b where -2 -3 2 4 2 A = 2 b = (10,5,4)" -2 -3 14. In case…

A: Given :-  Let a linear system of equations Ax =b where A = 42-222-3-2-314    ,      b = 10,5,4T To…

Q: Consider the system Jax + by = c lazx + bzy = c2. Use Cramer's Rule to prove that if the first…

A: Given system of equations are, a1x+b1y=c1a2x+b2y=c2 Using Cramer rule to find the solution of the…

Q: Return this to the familiar linear system 2х1 + х2 — ӕз + 2х4 3x2 – x3 + 2x4 -x3 + 4x4 = 2x4 -1 11…

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Q: Solve the following system of equations by LU decomposition: 8x1 + 4x2 - хз %3 11 -2x1 + 5x2 + x3 =…

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Q: Obtain the answer of the following linear equation system by Gaussian elimination method. -12 +2r3 =…

A: To solve the given system of equations by Gaussian elimination method.

Q: Show that the vector x = 0 3 is in the span of the vectors 3 ------C = y = 0 -3 2 W= 0 1/2 = 12 11

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Q: Use Cramer's Rule to solve the following system of linear equations 2л + 3у + 62 3 3 x + 2y + 2z =…

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Q: use Cramer's Rule to solve the given linear system 2x -y = 5   x + 3y = -1

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Q: Suppose the solution set of a certain system of linear equations can be described as x₁ = 5 + 3x3,…

A: Suppose the solution set of a certain system of linear equations can be described as x1=5+3x3,…

Q: By setting up and solving an appropriate system of linear equations, determine whether there is a…

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Q: Use Cramer's rule to solve the linear system of equations; 2x2 + 5x3 = 1 2x₁ + x₂ + x3 = 1 3x₁ + x₂…

A: Given equations are 2x2 + 5x3 = 12x1+x2+x3 = 13x1+x2 = 2

Q: Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).

A: Introduction: An equation of the plane passing through the points a0,b0,c0, a1,b1,c1, and a2,b2,c2…

Q: -3x1 + x2 + 12x3 = 50 6x1 – x2 – x3 = 3 6x1 + 9x2 + x3 = 40

A: Here we consider X1=x,  X2=y, X3=z (for Easier to solve) .  So,

Q: solve for w,x,y,z using Gaussian elimination

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Q: Use Cramer’s Rule to solve (if possible) the system of linear equations.

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Q: Suppose you want to interpolate the points (−1, −3), (0, 0) and (1, 3) by a polynomial. (a) What…

A: Given                                 t = x                                       y -1 -3 0 0…

Q: Solve the linear system Ax = b by Lu-Factorization showing CROUT's method. Show the complete…

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Q: a + 2b – c + 4d = 1 -a – 3b + 2c + 2d = 4 2a + 2b – c + 2d = 2 a + 2b +c = 1 using, a. Cramer's Rule

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Q: For each one of the following systems of linear equations: I) 20 8x1 + 3x2 12.x2 + 6x3 X1 + 10r3 30…

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

Q: A set of linear equations is: 5x - 2y + 3z = 16 and 19y - 7z+ 10 = 18 and 10z + 8y = 1. What are the…

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Q: Solve the given linear system using LU Decomposition

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Q: 1. 3X1 + 4X2 = -2 5X1 + 3X2 = 4

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

Q: 2 Which point makes both equations true (a solution of the linear system)? y= -x+3 and y= 4x- 2 A…

A: We have to find solution

Q: 3x 2х, +3к3 =0 X2 +2*3 =3 - 2x1 +*2-2

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Q: Create a 10 simultaneous linear equations with 10 variable unknowns in a, b, c, d, e, f, g, h, j, k…

A: Given: The variables are a, b, c, d, e, f, g, h, j, k. To write: The 10 simultaneous linear…

Q: 6. Consider the following system of four linear equations in five variables. 2x1 + 4x2 – 2x3 + 2x4 +…

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Q: Find the values of x1, x2, x3 in the system of Linear Equations 2x, – 6x, – x3 = -38 —3x, — х, + 7х,…

A: For easy understanding let x1 = ax2 = bx3 = c So the given equations are 2a-6b-c=-38  -3a-b+7c=-34…