The matrix equation (Ax b) A 1 0 1 2 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 (ie., write the system corresponding to the "normal equations") Preview Preview 2. The solution to the system of normal equations is Preview 3. The vector in the column space of A nearest to the vector b is Preview 4. The "error vector" (i.e., the...
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...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Find the least squares solution to the inconsistent system Ax = b 110- 110 3 A - b = 101 8 - [101܂ 2܂ ܘ a. 5 -3 0 ob. 7 2 8 + tl-3 11 l.- tec .6 0. 1 1 1 O d. -L 1 |t = ܐ + 5 -3 0 tec 1 1 5 1-'t = ܐ t tec 0 -1 5 x = tj-3 0 tec
Find the least squares solution to the inconsistent system Ax = b 3 A = 1 1 0 1 1 0 1 0 1 101] b = 8 2
Part A is first 2 lines, Part B is last 2 lines, thanks!
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y2(x) are linearly independent solutions ofthe corresponding homogeneous equation. Note: The cocfficient of y" must always be 1, and hence a preliminary division may be required y2(x) = x-2 ·y1(x) = x y2(x) = ex
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions...
Find the least squares solution to the inconsistent system Ax = b 1 1 0 110 3 A = b = 101 8 1101 2
9. IfA = -1 2 - 3 4 then eAt 3 et - 2 e2t -2 et + 2 e2 t 3 et - 3 e2 t -2 et + 3 e2 t a) (5 pts) What is de At A.eAt = ? dt b) (15 pts) Solve the system Yı - Y1 + 2 Y2 y2 - 3 yı + 4 y2 Yi (0) = 1, Y2 (0) -1. Extra Credit (10 pts) Then write down a particular solution...
Linear Algebra:
14. Let A=| 1 2 | and b=| 1 |. (1) Use the Existence and Uniqueness Theorem to show Ax = b is an inconsistent linear system. (2) Find a least-squares solution to the inconsistent system Ax = b.
14. Let A=| 1 2 | and b=| 1 |. (1) Use the Existence and Uniqueness Theorem to show Ax = b is an inconsistent linear system. (2) Find a least-squares solution to the inconsistent system Ax = b.
Let A e Rmxn. The linear system Ax = b can have either: (i) a unique solution, (ii) no solution, or (iii) infinitely many solutions. If A is square and invertible, there is a unique solution, which can be written as x = A-'b. The concept of pseudoinverse seeks to generalise this idea to non-square matrices and to cases (ii) and (iii). Taking case (ii) of an inconsistent linear system, we may solve the normal equations AT Ar = Ab...