Final answer:
The student is inquiring about the eigenvalues of a matrix and the process involves finding the roots of the characteristic polynomial resulting from the matrix subtracted by λ times the identity matrix.
Step-by-step explanation:
The student's question appears to relate to the eigenvectors and eigenvalues of a given matrix A. Particularly, they are interested in understanding the eigenvalues of the matrix A, which they have specified has an eigenvalue λ₁ = 1. The algebraic multiplicity of this eigenvalue is key in understanding how many times this eigenvalue appears in the characteristic polynomial of the matrix. The solution to the problem will involve calculating the determinant of the matrix subtracted by λ times the identity matrix and finding the roots of the resulting characteristic polynomial, which are the eigenvalues of the matrix A.