Find a fundamental matrix of the system y'=Ay for
A =
Find the fundamental matrix for the two-dimensional system defined by * = x, + txz, *2 = x2, and determine the solution for which x,(0= C1, x2(0) = C2.
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenvalues וג --1and Az--3 with corresponding eigenvectors u (1,1) and u2 (1,-1) (b) Sketch the trajectory of the solution having initial vector y(0) = ul. (c) Sketch the trajectory of the solution having initial vector y(0) -u2. (d) Sketch the trajectory of the solution having initial vector y(0)-u -u 1 U
4. Consider the system y'- Ay(t), for...
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental matrix for the given system of equations. Use the eigenvectors so that the coefficeints in the first row all equal 1 Equation Editor Ω Common Matrix Ψ (t) = (b) Find the fundamental matrix重(t) satisfying重(0) = 1. Equation Editor Ω Common Matrix tan a) sin(a) 0os(a) 重(t) =
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental...
(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
2. Suppose A-1103132 10 9-2 (a) What are the dimensions of the four fundamental subspaces associated with A? (b) Find a basis for each of the four fundamental subspaces. 3. Solve this linear system using an augmented matrix:
2. Suppose A-1103132 10 9-2 (a) What are the dimensions of the four fundamental subspaces associated with A? (b) Find a basis for each of the four fundamental subspaces. 3. Solve this linear system using an augmented matrix:
2. (5pts Determine whether the following set of vectors is a fundamental set of solutions of a system y' = Ay for some matrix A = A(t). / -et 0 y1 = -e- , y2 = -et, y3 = 0 I ett 2e-t 2e2
Consider the matrix transformation T:R → R given by T(x,y,z) = (x+ay, x+(a+1)y, x+ay+z) where a = 13. First use inverse of transformation to find T-(2,1,2). if T-(2,1,2)=(b,c,d) then b+c+d =
2. Find the augmented matrix of the linear system X – y + z = 7 x + 3y + 3z = 5 X – Y – 2z = 4 Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
(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) The general solution of the linear system y = - Ay is 0 Wt) = [ [E] O et/6 Determine the constant coefficient matrix A. A =