GATE XE (Engineering Sciences) 2023 - Question 18

Section: Engineering Mathematics | Marks: 2

Let 𝑃= [ 4 −2 2 6 −3 4 3 −2 3 ], and 𝑄= [ 3 −2 2 4 −4 6 2 −3 5 ] . The eigenvalues of both 𝑃 and 𝑄 are 1, 1, and 2. Which one of the following statements is TRUE?

• A. Both 𝑃 and 𝑄 are diagonalizable
• B. 𝑃 is diagonalizable but 𝑄 is NOT diagonalizable
• C. 𝑃 is NOT diagonalizable but 𝑄 is diagonalizable
• D. Both 𝑃 and 𝑄 are NOT diagonalizable

Answer: B. 𝑃 is diagonalizable but 𝑄 is NOT diagonalizable