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Linear systems: Problem 7 (8 points) Consider the linear system

`vec(y)^(')=[[-3,-2],[5,3]]vec(y).`

a. Find the eigenvalues and eigenvectors for the coefficient matrix. b. Find the real-valued solution to the initial value problem

```
y_(1)^(')=-3y_(1)-2y_(2),y_(1)(0)=-6,
y_(2)^(')=5y_(1)+3y_(2),y_(2)(0)=15.
```

Use

`t`

as the independent variable in your answers.

```
y_(1)(t)=
y_(2)(t)=
```