(1) Use the "Schoolboy's Trick" to find a system of two ODE (first order homo geneous linear, wit...
(1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. , and 12 = -:| b. For each eigenpair in the previous part, form a solution of ý' = Ay. Use t as the independent variable in your answers. ý (t) = and yz(t) = c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
(1 point) Consider the linear system "(-1: 1) y. a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 v1 = and 2 V2 b. For each eigenpair in the previous part, form a solution of y' = Ay. Use t as the independent variable in your answers. (t) = and yz(t) c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following form Hint: It is given that one of the solutions of the above system Useful formulas Case 1: A only have distinct roots for λ General solution is ,n) are the coresponding eigenvectors where K, (where i = 1,2, Case 2: For a system of n equations, the...
Find a description of the solution set of each system of linear equations below by car rying out the following steps. (i) Use Gaussian elimination to find the solution set S as you did in Chapter 1. (ii) Find a point Q and a set of points B:- (Pi. P2... so that S-Q+Span IB. (iii) show that B is a basis for L :--Span B. what is the dimension of the space L? (iv) Describe S as looking like either...