Final answer:
To find an eigenvector for a matrix, solve the equation (A - λI)v = 0. The eigenvectors can be expressed in component form using unit vectors. Without specific values, the exact eigenvectors cannot be determined.
Step-by-step explanation:
The student's question is about finding the eigenvectors associated with given eigenvalues of a matrix. To find an eigenvector for a particular eigenvalue, one must solve the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue, I is the identity matrix of the same size as A, and v is the eigenvector corresponding to eigenvalue λ.
As the question does not provide specific eigenvalues or the matrix itself, we cannot compute the exact eigenvectors.
However, if eigenvectors for certain eigenvalues are already given, one can simply rewrite these vectors in vector component form using the basis unit vectors.
For example, an eigenvector v could be expressed in component form as v = xi + yj + zk, where i, j, and k are the unit vectors along the x-, y- and z-axes respectively, and x, y, and z are the scalar components of the vector.