2. Calculate the following quantities using least-squares (give coefficients to three decimal places): (a) The least-squares solution to the inconsistent system x+3y=9, 3x+y=5, z + y = 2. (b) The least-squares line y = mx + b approximating the points {(4,7), (11,21). (15,29), (19,35), (30,49)}. (c) The least-squares quadratic y = ar²+bx+c approximating the points {(-2,22), (-1,11), (0,4), (1,3), (2, 13)}.

Q: Solve the following system of linear equations using L-U Decomposition Method. Assume U₁1 U22 = U33…

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Q: Q-2: [1 0 2 1 1 [1 -21 and B: [1 a) Let A 1 1 If possible, compute A + BT and [i 1 -1] 3 ВТА. X1 +…

A: According to our guidelines we can answer only one question and rest can be reposted.

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: We want to find the root of the following system of equations using the fsolve function in MATLAB:…

A: Given the system of non-linear equations,To solve this using the Matlab, we perform the following…

Q: Express the following system of linear equations as a vector equation. 1x1 +4x2 - 6x3 = -5 -2x1 +…

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Q: 2x1 – 3x2 = 1 Ox1 + 0x2 = 2

A: For the system in the figure above  we Find a solution of least squares.

Q: Find the least-squares solution for a and b in the four equations 2 = a + b 4 = 3a +b 1= 2a + b 4 =…

A: Given equations are2=a+b4=3a+b1=2a+b4=4a+bThe least-squares solution for a and b in the four…

Q: ) Find the third-order polynomial with the least squares solution that will give the best…

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Q: Express the following system of linear equations as a vector equation. x₁+ x2+ J 5x1 + 1x2 -7x1 +…

A: Solution :

Q: Is there a real number x such that x = 2-x? Decide by displaying graphically the system

A: Consider the equation: x=2-x. Is there a real number x satisfying the equation.   If the graphs of…

Q: Solution of an (r, q) system yields the optimal values as (r, q) = (47, 115). Based on these…

A: Solution: Given "r" is the replenishment level which is equivalent to "s"which is reorder level. "q"…

Q: x1 + 2x2 + 3x3 = 6 2х1 - 3x2 + 2x3 = 14 3x1 +x2-x3 =-2

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Q: Consider the data table x -1 0 1 2y -1 2 -2 0Compute and simplify the interpolating polynomial by…

A: The objective of this question is to find the interpolating polynomial for the given data points…

Q: The vector (1,-2, –3) is a solution of the linear system: X1 + 3x2 - 3x3 = -2 5x1 + 13x2 - 13x3 = -8…

A: We have to solve the problem

Q: Given a set of points, the least-squares line formed by letting xbe the independent variable will…

A: Given: Given a set of points, the least-squares line formed by letting xbe the independent variable…

Q: 10.5 Solve the following system of equations using LU factorization with partial pivoting: 2x₁6x₂x₂=…

A:

Q: Given the data (1, 2), (3, 7), and (5,50): (a) Fit a straight line of the form to these values by…

A: As per guidelines we will solve first question only, please repost other questions for more answers.…

Q: Determine the least-squares solution to the following: -3 0 0 2 1 1 2 -2 - 1 1 30 X X 1 2 X 3 1 0 2…

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Q: Find the set of all solution vectors of the following system of linear equations and write in form X…

A: Given that the system of linear equations  2 x1-x2+3 x3=-34 x1+2 x2- x4=1

Q: Please answer step by step and write clearly

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Q: x1 + 2x2 + 3x3 = 6 2х1 - 3х2 + 2x3 = 14 3x1 +x2-x3 =-2

A:

Q: 4x2 3 %| 4x2 - 5 - Find the least-squares solution to the singular system: 1 - 5x1 + 4x2 X2 =

A:

Q: In the order of the data given in the following table, write a system of linear equations in terms…

A: Given that

Q: Find the LU factorization of -3 A = -15 -6 such that the main diagonal of \left[ -4 3 -21 16 -10 10…

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Q: Find the least-squares solution of the system fe || II 1 3 2 4 x 6 E 16

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Q: 5x, + x, + x, + X; 2х, - х, + х, + бх, = 11.25 X, + x, + 4x, - x, = 7 X, - 7x, + x, - x, + x, =…

A: For convenience we take x1=u, x2=v, x3=x, x4=y, x5=z.

Q: x + 3y = 2 2х + у %3-1 X - 3x - y = 3

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Q: Consider the following system of equations: The solutions of (*) are x = x + y + z = 2 x + 3y +3z=0…

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Q: The following system has the following pivot variables. ..? 2 – 2x, – 3x, – 6x3 - 5x4 + 2x5 = 7 X3 +…

A: Hence option (a) is correct.

Q: 2. Evaluate for the unknown variables Using the following, (a) Gauss-Jacobi Method (b) Gauss- Seidel…

A: (a) Let X1=x, X2=y, X3=z By Gauss-Jacobi Method Total Equations are…

Q: x₁ + 2x₂ + 3x3 = 6 2x13x2 + 2x3 = 14 3x₁ + x₂ - x₂ = -2

A: We have to solve the given system of equations using Cramer's rule.

Q: (a) Show that 1 1 1 1 1+ x 1+ 2x = 2x3 (1 + x)² (1+ 2x)² | Hint: Performing row operations will save…

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…