Question

Consider two matrices: $P = \begin{bmatrix} 1 & 2 \\\ 0 & 1 \end{bmatrix}$ and $Q = \begin{bmatrix} 1 & 0 \\\ 0 & 1 \end{bmatrix}$. Which of the following statements is/are true?

• A. P and Q have same set of eigenvalues
• B. eigenvalues P and Q commute with each other
• C. P and Q have different sets of linearly independent eigenvectors
• D. P is diagonalizable

Answer 1

Answer: (A), (B), (C)

P and Q have same set of eigenvalues

Answer 2

The correct Answers are (A) :P and Q have same set of eigenvalues (B):eigenvalues P and Q commute with each other (C):P and Q have different sets of linearly independent eigenvectors