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4. (4) Fitting (in the least-square sense) the best parabola b=C + Dt + Et? through...
»lem 2(*): Suppose that we want to find the best equation of the form y -c c2t + 2 C3 sin(nt to d...
»lem 2(*): Suppose that we want to find the best equation of the form y -c c2t + 2 C3 sin(nt to describe some observed data we are given the data points IA , , за , 0 where each entry is of the form Our goal is to find the best solutions in the least squares sense. » Set up the system of equations in variables c1, c2, c3 determined by the data points Write the system in matrix...
2. This problem finds the curve C ++D = b which gives the best least squares...
2. This problem finds the curve C ++D = b which gives the best least squares fit to the points: t= -2, b=0 t = -1, b=0 t= 0, b=1 t= 1, b=1 t= 2, b=1 (a) (10 points) Write down the 5 equations Ax = b that would be satisfied if the curve went through all 5 points. (b) (10 points) Find the least squares solution = (Ĉ, Ð). (c) (10 points) Find the projection p of b onto...
Given the data (t1, b) = (-1,-4) (t2, b2) = (0,2) (t3, 63) = (1,2) (t4,64)...
Given the data (t1, b) = (-1,-4) (t2, b2) = (0,2) (t3, 63) = (1,2) (t4,64) = (2, -7), find the linear equation f(t) = cit+co that best fits f(ti) = bị. a.(5 points) Find the matrix A for which you can rephrase the problem as solving Ax* 2 2 -7 7 C1 for which x* = [e gives the least-square solution. Со b.(15 points) Solve the least-square problem and find cit+ Co.
3 and 4 The matrix equation (Ax b) -1 -2 -1 1 2 2 0 1 has no solution. We wish to find the best approximate solution to...
3 and 4
The matrix equation (Ax b) -1 -2 -1 1 2 2 0 1 has no solution. We wish to find the best approximate solution to this system 1. Write the system of equations used to find the best approximation (i.c., write the system corresponding to the "normal equations"). Preview Preview 2. The solution to the system of normal cquations is Preview 3. The vector in the column space of A nearest to the vector b is Preview...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vect...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vector subspace W of R" such that Rn and an (a) Describe all the affine subspaces of IR2 which are not vector subspaces of R2 (b) Consider A e R"Xn, beR" and the system of linear equations Ar- b. Prove that: (i) if A-b is consistent, then its solution set is an affine subspace of R" with underlying (ii) if...
Problem 5. A subset A c Rn is an affine subspace of Rn if there exists a vector b є R', and a und...
Problem 5. A subset A c Rn is an affine subspace of Rn if there exists a vector b є R', and a underlying vector subspace W of Rn such that (a) Describe all the affine subspaces of R2 which are not vector subspaces of R2. (b) Consider A є Rnxn, b є Rn and the system of linear equations Ax-b Prove that (i) if Ar= b is consistent, then its solution set is an affine subspace of Rn with...
2. Suppose that you were to try to find a parabola y az2 +bz c that passes through the (x, y) pairs (-4,7), (-1,-3), and (1,6). To obtain the coefficients a, b, and c you would try to solve a system...
2. Suppose that you were to try to find a parabola y az2 +bz c that passes through the (x, y) pairs (-4,7), (-1,-3), and (1,6). To obtain the coefficients a, b, and c you would try to solve a system of linear equations whose augmented matrix is which of the following? 16 -4 1 49 16 -4 1 7 (a)9-1-3(b)11 1 9(1-1 1 -3 36 1 1 6 49 7 1 16 (d)1 -3 1-1(e)9 3 1 1 36...
Using Octave to solve (preferably with solving the differential equations and go through the process) 1. A harmonic osc...
Using Octave to solve (preferably with solving the differential
equations and go through the process)
1. A harmonic oscillator obeys the equation dx dt dt which can be written as a set of coupled first order differential equations dx dt dt One procedure in Octave for coding these equations involves a global statement and the line solutionRC Isode(@dampedOscillator, [1, 0], timesR); Employ the help system to determine the properties of the Isode() function (or an equivalent solver such as ode23()...
The area of the parallelogram formed by vectors a=(−1,3,1) and b=(1,2,0), rounded to one decimal, is:...
The area of the parallelogram formed by vectors a=(−1,3,1) and b=(1,2,0), rounded to one decimal, is: Select one: a. 5.4 b. 5.5 c. -6.0 d. none of above Find the component of the vector with initial point (2,−1,1) and terminal point (4,3,−6): Select one: a. (2,4,−7) b. (6,3,−5) c. (8,−3,−6) d. (−2,−4,7) Determine whether the statement is True or False: The sum of two invertible matrices of the same size must be invertible. Select one: a. True b. False Determine...
»lem 2(*): Suppose that we want to find the best equation of the form y -c c2t + 2 C3 sin(nt to describe some observed data we are given the data points IA , , за , 0 where each entry is of the form Our goal is to find the best solutions in the least squares sense. » Set up the system of equations in variables c1, c2, c3 determined by the data points Write the system in matrix...
2. This problem finds the curve C ++D = b which gives the best least squares fit to the points: t= -2, b=0 t = -1, b=0 t= 0, b=1 t= 1, b=1 t= 2, b=1 (a) (10 points) Write down the 5 equations Ax = b that would be satisfied if the curve went through all 5 points. (b) (10 points) Find the least squares solution = (Ĉ, Ð). (c) (10 points) Find the projection p of b onto...
Given the data (t1, b) = (-1,-4) (t2, b2) = (0,2) (t3, 63) = (1,2) (t4,64) = (2, -7), find the linear equation f(t) = cit+co that best fits f(ti) = bị. a.(5 points) Find the matrix A for which you can rephrase the problem as solving Ax* 2 2 -7 7 C1 for which x* = [e gives the least-square solution. Со b.(15 points) Solve the least-square problem and find cit+ Co.
3 and 4
The matrix equation (Ax b) -1 -2 -1 1 2 2 0 1 has no solution. We wish to find the best approximate solution to this system 1. Write the system of equations used to find the best approximation (i.c., write the system corresponding to the "normal equations"). Preview Preview 2. The solution to the system of normal cquations is Preview 3. The vector in the column space of A nearest to the vector b is Preview...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vector subspace W of R" such that Rn and an (a) Describe all the affine subspaces of IR2 which are not vector subspaces of R2 (b) Consider A e R"Xn, beR" and the system of linear equations Ar- b. Prove that: (i) if A-b is consistent, then its solution set is an affine subspace of R" with underlying (ii) if...
Problem 5. A subset A c Rn is an affine subspace of Rn if there exists a vector b є R', and a underlying vector subspace W of Rn such that (a) Describe all the affine subspaces of R2 which are not vector subspaces of R2. (b) Consider A є Rnxn, b є Rn and the system of linear equations Ax-b Prove that (i) if Ar= b is consistent, then its solution set is an affine subspace of Rn with...
2. Suppose that you were to try to find a parabola y az2 +bz c that passes through the (x, y) pairs (-4,7), (-1,-3), and (1,6). To obtain the coefficients a, b, and c you would try to solve a system of linear equations whose augmented matrix is which of the following? 16 -4 1 49 16 -4 1 7 (a)9-1-3(b)11 1 9(1-1 1 -3 36 1 1 6 49 7 1 16 (d)1 -3 1-1(e)9 3 1 1 36...
Using Octave to solve (preferably with solving the differential
equations and go through the process)
1. A harmonic oscillator obeys the equation dx dt dt which can be written as a set of coupled first order differential equations dx dt dt One procedure in Octave for coding these equations involves a global statement and the line solutionRC Isode(@dampedOscillator, [1, 0], timesR); Employ the help system to determine the properties of the Isode() function (or an equivalent solver such as ode23()...
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