1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10 (11 points) The matrix A= 2 1 3 2 7 reduces to R= 0 3 1 a 6 5 0 1 Let ui, , 13, 144, and us be the columns of U. (a) Determine, with justification, whether each of the following sets is linearly independent or linearly dependent. i. {u1, 12, 13) ii. {u1, 13, us} iii. {u2, 13} iv. {u1, 12, 13,...
Find the general solution. 2. Find the general solution. X' = AX A= 1 1 0 1 0 1 0 1 1 Note: X = [X1 22 23 x3]".
(33 pts) This question is about the matrix = ſi 2 [3 2 0 4 1 6 3 1] 4 9 co (a) Find a lower triangular L and an upper triangular U so that A = LU. (b) Find the reduced row echelon form R = rref(A). How many independent columns in A? (c) If the vector b is the sum of the four columns of A, write down the complete solution to Ax = b
Find the general solution of the equation: y'' + 5y = 0 Find the general solution of the equation and use Euler’s formula to place the solution in terms of trigonometric functions: y'''+y''-2y=0 Find the particular solution of the equation: y''+6y'+9y=0 where y1=3 y'1=-2 Part 2: Nonhomogeneous Equations Find the general solution of the equation using the method of undetermined coefficients: Now find the general solution of the equation using the method of variation of parameters without using the formula...
A =10 ſi -2 -5 4 3 11 Jo 0 1 -2 0 -4 0 0 0 0 1 3 Lo 0 0 0 0 0 ] Describe all solutions of Ax = 0. x = x2 + 4
2d and 4b [2 リ 5 0 -6 200 x(0)=10 x' e2 0 0 |-6-1 3 0 42 0-1-2 x, 43,1 0 0 (d) x' = ' x' (c) x'=12-1-2|x; 2. The matrices in the following systems have complex eigenvalues; use Theorem 2 to find the general (real-valued) solution; if initial conditions are given, find the particular solution satisfying them. 1-x, x(0)-1 (b) x, = (a) x' = X; 0 20 x(0)-|2 이 x, (d) x'=1-20 (c) x' =10-1-6|x; L0...
4. (3 points) Let ſi 2 1] A= 0 4 3 [1 2 2 Compute the third column of A-1 by solving the equation Ax = es, where ez = 0 Hint: Use Cramar's rule to solve the equation, noticing that the third column of A-' is given by the solution of the above equation. In fact there is nothing special about A-1, the third column of any 3 x 3 matrix B is given by the product Bez. Can...
Find the general solution. Please and thanks. 2. x'(t) = 0 1 1 1 0 0 1 2(t) 1 1 0 1 3. x'(t) = 1) =(t) i 1 -i
Find the general solution of the given system. 5 -1 2 -1 0 5 x(t) = eBook Find the general solution of the given system. 5 -1 2 -1 0 5 x(t) = eBook
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0 1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0