Some US census population data is given in the following table year 1980 1990 2000 population (y) 227 249 281                        Here population is given in millions. 1. Fit a second degree polynomial passing through these points. 2. Use it to predict population in year 2010 and 2020. Note: Develop the linear system of equations from the above theory and solve the system by LU Decomposition Method(note: its linear algebri related question solve using lu decomposition method)

Q: Exercise 1.4.19 Solve the system of equations 9x-2y+4z=-17, 13x-3y+6z=-25, and -2x-z = 3.

A: The given system of equations

Q: Year 1980 1990 2000 Population y Here population is given in millions. 227 249 281 1. Fit a second…

A: Note that the LU decomposition will depend on the choices of the initial point of t. As we have…

Q: -8x1+3x2-6x3+2x4 = -5 %3D 5x1+6x2+2x3-4x4 = -8 %3D -3x1 +2x2-7x3+5x4 = 4 4x1 -5x2+3x3-6x4 = 9 Solve…

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Q: Q.1 Solve the following system of equations using Cholesky decomposition method. 4x₁ + x₂ - X3 = 7,…

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Q: Urgen

A: Given, r0+3r1x1+3r2x12=y1r0+3r1x2+3r2x22=y2r0+3r1x3+3r2x32=y3 This can be written in Vandermonde…

Q: 3. Find the solution to the following system of linear equations using LU decomposition of the…

A: Note: '' As per guidelines we will solve the first question. If you want any specific question to be…

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

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Q: Some US census population data is given in the following table. Year Year 1980 1990 2000 Population…

A: The year 1980, 1990 and 2000 corresponding to x=0, x=10 and x=20. Thus, the points are (0,227),…

Q: 1. Consider P(x) = 9x3 – 39x? + 46x – 16 and B(x) = 3x – 8. P(x) Part A: Determine B(x)' Part B:…

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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: Solve the system Ax=b using the given LU factorization of A.…

A: Given LU factorization of A.  A=6-235=101216-206 and b=012 We have to solve Ax=b.

Q: -8x1+3x2-6x3+2x4 = -5 %3D 5x1+6x2+2x3-4x4 = -8 -3x1 +2x2-7x3+5x4 = 4 4x1 -5x2+3x3-6x4 = 9 Solve the…

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Q: 3. Solve the following system using LU-decomposition: 2x1 +8x=-2 21-22-2

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Q: Question 5 Ps) Solve the following linear system (a) 7x₂ + 2x₂-3x₂ = - 12 2x₂5x₂ 3x3 = -20 <-26 x₁ -…

A: Since you have posted a multiple question according to guildlines I will solve first(a)   question…

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: Suppose experimental data are represented by a set of points in the plane. An interpolating…

A: Given interpolating polynomial is p(t)= a0+a1t+a2t2 for the data (1,14),(2,18),(3,20)Putting the…

Q: Solve system of linear algebraic equations -10 -5 10 by the LU- decomposition method with a unit…

A: As peth the question we are given a linear system Ax = b where A, b are given and we have to solve…

Q: • Solve the given system of equations below by applying Doolittle decomposition to the coefficient…

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Q: x, + 2x, + 5x, - x, = -1.75 X - 6x, + x, + x, + x, = 9.25 – 5x, + x2 - X, + X, + X; = 4.25 2x, - x,…

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Q: Please answer step by step and write clearly

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Q: System of Linear Equations (Iterative Methods) Iterative methods ave based on successive Improvement…

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Q: Solve the following system of equation using matrix inversion with LU Decomposition method: -8x₁ +…

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Q: Solve the following Systems of Non-Linear Equations. Using the following methods: 1. Gauss-Seidel…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

Q: (a) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the height in…

A: Since you've asked multiple questions, as per the answering guidelines we are supposed to answer one…

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: Ise the LU decomposition to solve 3 1 6. -6 0 -16 12 4. 08 -17 I3 17

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Q: Suppose experimental data are represented by a set of points in the plane. An interpolating…

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Q: Which of the following is a factor of 2x2 -I- 6? O 2x 3 Oz-3 Oz- 2 O2x + 1

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Q: let A nonsingular matrix, k positive integer then (A5 Select one: k+1 k-1 b. (A,*1

A: As per the policy i can solve only first question for you, fore remaining question you can post them…

Q: 2. Use Gauss elimination with back substitution to solve the system of linear equations: 8x, +x,…

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Q: When the following system of equations is solved using LU decomposition, 4x1 - 10x3 =1 2x1+ X2+ X3=…

A: We can solve the given problem using the concept of system linear equations.

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: Use LU-decomposition method to find the solution of the linear system: +2x, +3x3 = 6, 2.x, + 7x, +…

A: Given AX = B where                A = 12327114-6X = x1x2x3B = 6131 Let A = LU, where          L =…