4. Let A = (3 2 2 2 3-2 (a) Using any method, determine A¹. (b) Using A¹, find the least squares solution of the least norm, of the system Az = b, given b = (1,−1)². (c) Find all the solutions of Az = b.
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- The coefficient matrix is not strictly diagonally dominant, nor can the equations be rearranged to make it so. However, both the Jacobi and the Gauss-Seidel method converge anyway. Demonstrate that this is true of the Gauss-Seidel method, starting with the zero vector as the initial approximation and obtaining a solution that is accurate to within 0.01.Show complete solution using First Order Linear DE and Bernoulli DEFind a formula for the least-squares solution of Ax =b when the columns of A are orthonormal.
- 6. i reposted it again because i wanted this in detailed not in online calculator, thanksFind the solution of the following Homogeneous Linear DE of Higher Order.Find the general solution of the linear system (1) when A is then x n diagonal matrix A = diag[Aj, A21... ,An]- What condition onthe eigenvalues Al, ... , An will guarantee that limt_,,. x(t) = 0 for allsolutions x(t) of (1)?You are given 6 data points (xi; yi) below, where i = 1,..., 6 that are observed from a model: y = a3x3 + a2x2 + a1x + a0 + n, where n is a zero-mean Gaussian noise. Estimate the coefficients: a0,...,a3 by setting up a linear system of equations, and solving it using least squares. (x1,y1) = (-3, -171.17478734011377) (x2, y2) = (-1.5, -26.283603386675573) (x3, y3) = (0, 10.342025892375206) (x4, y4) = (2, 34.71284310507833 (x5, y5) = (5.5, 733.5702844691194) (x6, y6) = (7, 1546.4530015969324)
- Can I get some help with this "finding a pseudoinverse" problem?Find A+ and use it to compute the minimal length least squares solution to Ax = b.A certain experiment produces the data (0, 1),(−1, 2),(1, 0.5),(2, −0.5). Find values for a, b, and c which describe the model that produces a least squares fit of the points by a function of the form f(x) = ax2 + bx + c.