(a) (b) (c) (d) Consider the following linear system: 2 -1 2x -60-2 (1) (ii) (i)...

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(a) (b) (c) (d) Consider the following linear system: 2 -1 2x₁ -60-2₂ (1) (ii) (i) (ii) Given the following system of equations: 7w-2x+y+2z=3 f(x) (i) 13-0 8-1 5x3 Use row reduction technique to find an upper triangular U and lower triangular L in the LU factorization of the given linear system. [2.5 marks] (ii) Then find the values of x₁, x2 and x, by using the L and U obtained from (i). [3 marks] 2w+8x+3y+z =-2 -w+5y+2z=5 2x-y + 4z= 4 Construct the equations for w, x, y and z of the above linear system using Jacobi Method. [2 marks] n 0 1 Consider the following data: x Copy the following table into your Answer Booklet. Complete it by computing one iteration of the Jacobi Method for the constructed equations in (i) starting with [w, x,y,z] = [0, -1, 1, 1]. Write your answers correct to FOUR decimal places. [2 marks] Z 1 Determine whether = -7 is the eigenvalue of matrix A= W 0 X -1 x₂ = 1 3 x₁ = 2 5 y 1 [2 3 3-6 [1.5 marks] x₂ = 3 4 Construct the Lagrange Coefficients L, (x), L (x) and L₂ (x). [1.5 marks] Find the second interpolating polynomial P(x) using the results from (i). [1 mark] (iii) Approximate the value of f(1.5) from the P(x) obtained in (ii). [0.5 mark] Continued... (a) (b) (c) (d) Consider the following linear system: 2 -1 2x₁ -60-2₂ (1) (ii) (i) (ii) Given the following system of equations: 7w-2x+y+2z=3 f(x) (i) 13-0 8-1 5x3 Use row reduction technique to find an upper triangular U and lower triangular L in the LU factorization of the given linear system. [2.5 marks] (ii) Then find the values of x₁, x2 and x, by using the L and U obtained from (i). [3 marks] 2w+8x+3y+z =-2 -w+5y+2z=5 2x-y + 4z= 4 Construct the equations for w, x, y and z of the above linear system using Jacobi Method. [2 marks] n 0 1 Consider the following data: x Copy the following table into your Answer Booklet. Complete it by computing one iteration of the Jacobi Method for the constructed equations in (i) starting with [w, x,y,z] = [0, -1, 1, 1]. Write your answers correct to FOUR decimal places. [2 marks] Z 1 Determine whether = -7 is the eigenvalue of matrix A= W 0 X -1 x₂ = 1 3 x₁ = 2 5 y 1 [2 3 3-6 [1.5 marks] x₂ = 3 4 Construct the Lagrange Coefficients L, (x), L (x) and L₂ (x). [1.5 marks] Find the second interpolating polynomial P(x) using the results from (i). [1 mark] (iii) Approximate the value of f(1.5) from the P(x) obtained in (ii). [0.5 mark] Continued...

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a i To find an upper triangular matrix U and a lower triangular matrix L for the given linear system we perform LU decomposition on the coefficient matrix The coefficient matrix A is A 2 1 2 6 0 2 8 1 ... View the full answer