Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 24/Solution 1
Following the hint, the diagonal matrix is the eigenvalues and the column of are the are the corresponding right eigenvectors.
Therefore, A has 3 eigenvalues: , , , and their corresponding eigenvectors are , , . The eigenvectors in are normalized so that the 2-norm of each one is .
So is wrong. We have
is wrong. We have
is correct. A has three different eigenvalues and hence the three eigenvectors are independent, and they can form a set of basis.
is correct. is a scalar multiples of the last column vectors of . The scalar multiplication of any eigenvector is a eigenvector as well, so is correct
Thus, the answer is .