Question

The matrix [−1320−69] has eigenvalues λ₁=−1 and λ₂=−3.

Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥

Find the solution to the linear system of differential equations [x′₁ x′₂]=[−13 20−6 9][x₁ x₂] satisfying the initial conditions [x₁(0)x₂(0)]=[6−9].

x₁(t)= ______ x₂(t)= _____

Answer 1