Final answer:
To find the set of three normalized eigen vectors for a matrix, we need to find the eigenvalues and eigenvectors. The eigenvalues are the values of λ that satisfy the equation det(A - λI) = 0. The eigenvectors can be found by solving the equation (A - λI)v = 0. The eigenvectors can then be normalized to find the set of three normalized eigen vectors.
Step-by-step explanation:
To find the normalized eigen vectors for the given matrix:
Step 1: Find the eigenvalues of the matrix.
Eigenvalues are the values of λ that satisfy the equation det(A - λI) = 0, where A is the given matrix and I is the identity matrix. Using this equation, we can find that the eigenvalues are λ = 1, 5.
Step 2: For each eigenvalue, solve the equation (A - λI)v = 0 to find the corresponding eigenvectors.
Substituting the eigenvalue λ = 1 into the equation (A - 1I)v = 0, we get the eigenvector v1 = (1, -2, 1).
Substituting the eigenvalue λ = 5 into the equation (A - 5I)v = 0, we get the eigenvector v2 = (1, 1, 0).
Therefore, the set of three normalized eigenvectors for the given matrix are:
{v1, v2, (normalized v2)}