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3. Two solutions of the following linear equation system are x1, X2, where Xi = (1,1,-3,1), x2-x1...
(1 point) Do the following for the points (-3,1), (-2,2),(-1,1), (1,-2), (3,-2): (If you are entering...
(1 point) Do the following for the points (-3,1), (-2,2),(-1,1), (1,-2), (3,-2): (If you are entering decimal approximations, enter at least five decimal places (a) Find the equation for the best-fitting parabolay.2 +ba c for these points: y0.0139x*2-0.6887x-0.209 (b) Find the equation for the best-fitting parabola with no constant term y2b for these points: (c) Find the equation for the best-fitting parabola with no linear term yc for these points: 0.414xA2-0.6805x Ch5.2b Least Squares and Curve Fitting: Problem 5 Previous...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1 + 2x2 –x3= 18, x1 + 3x2+ x3 = 16, has the solution x=(3, 4,2)T. Using the initial guess x (0)=(1, 1,1)T Solve the above system as is using: Gauss-Seidel method. If the error increases, what does that mean and what should you do? (see b below) Condition the system so that convergence is secured and solve using the Gauss-Siedel method. Q2: Find a system...
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 =...
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 = X 1 + x2 + 6x3 = —2x1 + 8x2 + 4x3 = 3 (a) (3 pts) Write it in the form of Ax = b (b) (12 pts) Find all solutions of the system using Gauss elimination method. Write your answer as a column vector. (c) (4 pts) Use matrix multiplication to check your answer if possible. (d) (10 pts) Use Cramer's rule...
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1...
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1 + X2 = = [ 3 5 (Keep the equations in order.) -Xi+ X2 = _ x1 + X2 = Answer(s) submitted: (incorrect) 2. (1 point) Determine which of the points (1, -2, -2), (-7,3,3), and (6,1,-5) lie in the plane x1 - 4x2 +6x3 = -1. Answer: Answer(s) submitted: (incorrect)
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1...
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1 + X2 = = [ 3 5 (Keep the equations in order.) -Xi+ X2 = _ x1 + X2 = Answer(s) submitted: (incorrect) 2. (1 point) Determine which of the points (1, -2, -2), (-7,3,3), and (6,1,-5) lie in the plane x1 - 4x2 +6x3 = -1. Answer: Answer(s) submitted: (incorrect)
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 =...
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
matlab 1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a...
matlab
1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a code to find the solution of linear equations using a) Gauss elimination method b) Gauss-Seidel iterative method c) Jacobi's iterative method d) Compare the number of iterations required for b) and c) to the exact solution Assume an initial guess of the solution as (X1, X2, X3, X4) = (0,0,0,0).
Consider the following system of linear equations. x1 + 2x2 = 2 x1 – x2 = 2 x2 = 1
Consider the following system of linear equations. x1 + 2x2 = 2 x1 – x2 = 2 x2 = 1 (a) Give a brief geometric interpretation of the solution set of the system. (b) By hand, find the RREF of the augmented matrix of the system, indicating the row operations you are using at each step. (c) Is the system consistent? (d) Find the solution set of the system.
Determine the number of integer solutions of x1 + x2 + x3 + x4-32, where a)...
Determine the number of integer solutions of x1 + x2 + x3 + x4-32, where a) xi 2 0, 1 3is4 b) x1, x2 2 2, x3, X4 2 1
(1 point) Do the following for the points (-3,1), (-2,2),(-1,1), (1,-2), (3,-2): (If you are entering decimal approximations, enter at least five decimal places (a) Find the equation for the best-fitting parabolay.2 +ba c for these points: y0.0139x*2-0.6887x-0.209 (b) Find the equation for the best-fitting parabola with no constant term y2b for these points: (c) Find the equation for the best-fitting parabola with no linear term yc for these points: 0.414xA2-0.6805x Ch5.2b Least Squares and Curve Fitting: Problem 5 Previous...
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 = X 1 + x2 + 6x3 = —2x1 + 8x2 + 4x3 = 3 (a) (3 pts) Write it in the form of Ax = b (b) (12 pts) Find all solutions of the system using Gauss elimination method. Write your answer as a column vector. (c) (4 pts) Use matrix multiplication to check your answer if possible. (d) (10 pts) Use Cramer's rule...
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1 + X2 = = [ 3 5 (Keep the equations in order.) -Xi+ X2 = _ x1 + X2 = Answer(s) submitted: (incorrect) 2. (1 point) Determine which of the points (1, -2, -2), (-7,3,3), and (6,1,-5) lie in the plane x1 - 4x2 +6x3 = -1. Answer: Answer(s) submitted: (incorrect)
1. (3 points) Express the following vector equation as a system of linear equations. 4 X1 + X2 = = [ 3 5 (Keep the equations in order.) -Xi+ X2 = _ x1 + X2 = Answer(s) submitted: (incorrect) 2. (1 point) Determine which of the points (1, -2, -2), (-7,3,3), and (6,1,-5) lie in the plane x1 - 4x2 +6x3 = -1. Answer: Answer(s) submitted: (incorrect)
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
matlab
1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a code to find the solution of linear equations using a) Gauss elimination method b) Gauss-Seidel iterative method c) Jacobi's iterative method d) Compare the number of iterations required for b) and c) to the exact solution Assume an initial guess of the solution as (X1, X2, X3, X4) = (0,0,0,0).
Determine the number of integer solutions of x1 + x2 + x3 + x4-32, where a) xi 2 0, 1 3is4 b) x1, x2 2 2, x3, X4 2 1
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