Use your knowledge of eigenvalues and eigenvectors to answer the following questions. (a) (5 points) Find the eigenvalues and corresponding eigenvectors of the following matrix. (2 7 −1 −6) (b) (5 points) Consider the system y′ = (−15 −18 9 12)y It has eigenvalues/vectors of λ1 = −6, v1 = (−2 1) and λ2 = 3, v2 = (1 −1). What is the general solution for this system?
![Consider the linear system y→′ = [−3 −2 5 3]y→. a. Find the eigenvalues and eigenvectors for the coefficient matrix. λ1 = , v→1 = [ ], and λ2 = , v→2 = [ ] b. Find the real-valued solution to the initial value problem {y1′ = −3y1 − 2y2, y1(0) = −2 y2′ = 5y1 + 3y2, y2(0) = 5 Use t as the independent variable in your answers. y1(t) = y2(t) =](https://www.doubtrix.com/uploads/editor/6174151511mUCFTgrlOM.png)
