Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 24/Solution 1

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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 .