Math 54 quiz 11 express the given system of differential

Question

MATH 54 QUIZ 11-

 

1. Express the given system of differential equations in matrix notation.

 

x'₁ = -2x₂ + x₁ - 4x₃

 

x'₂ = 3x₃ + x₂ - x₁

 

x'₃ = -x₁ + 2x₃ - 3x₂

 

2. Find a 4 × 4 matrix A with constant coefficients such that x(t) = is a solution to x'(t) = Ax(t).

 

3. Show that the following collection of vector-valued functions is linearly independent on R:

 

 

4. Find a general solution of the system x'(t) = Ax(t), where A =

 

5. Find the solution to the system x'(t) = x(t) which satisfies x(0) =