Answer and Explanation:
To determine the corresponding eigenvalues of the matrix A, we need to solve the equation Av = λv, where v is an eigenvector and λ is the corresponding eigenvalue.
Given that v1 = [-3, 1] and v2 = [-10, 3] are eigenvectors of matrix A, we can substitute these values into the equation Av = λv:
For v1 = [-3, 1]:
A * v1 = λ * v1
[11 -3; 3 -8] * [-3; 1] = λ * [-3; 1]
Simplifying the equation, we get:
[-42 + 3; -9 + 8] = λ * [-3; 1]
[-39; -1] = λ * [-3; 1]
From the equation, we can see that λ must satisfy the following:
-39 = -3λ
-1 = λ
Therefore, the corresponding eigenvalue for v1 is λ1 = -3 and for v2 is λ2 = -1.
Hence, λ1 = λ2 = -3 and -1.