Question

Given that v1​=[−31​] and v2​=[−103​] are eigenvectors of the matrix A=[11−3​30−8​] determine the corresponding eigenvalues. λ1​=λ2​=​

Answer 1

Answer and Step-by-step 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.