Use the fundamental matrix Φ to find C1 and C2. You can use technology to do matrix operations

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

For this quiz (worth 10 points), you can use Wolfram Alpha to check your answers AND to do matrix inverses, BUT indicate where you do so. (Say: “ I got Φ-1 from W-alpha.”) 

We will be assessing your work not just on whether the final answer is correct, but on whether you can justify each step. This problem involves finding not just a general solution, but specific C1 and C2 to satisfy initial values using Φ-1. Remember that Φ is made with the two independent solutions: the thing multiplied by C1 and the thing multiplied by C2.. These "things" involve not just the eigenvectors, but also exponentials, sometimes times t, sometimes cos and sin, depending on the type of eigenvalues.

 Solve the following system with given initial conditions. Use the fundamental matrix Φ to find C1 and C2. You can use technology to do matrix operations and to check your results, but indicate where technology was used, and explain all the steps to find the eigenvalues, eigenvectors, the fundamental matrix, and the initial value constants.

 

 x′ = y                                       x (0) = 1

 

{y′ = − 4x + 4y                      {y (0) = 1

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