Question: Problem 3 3 i) What are the eigenvalues of 01 ? Is this matrix invertible? 0 0 1 O 0 O Is this matrix diagonalizable?

Problem 3 3 i) What are the eigenvalues of 01 ? Is this matrix invertible? 0 0 1 O 0 O Is this matrix diagonalizable? 5 ii) Let A 2 Are A and B similar? 0 4 and B - [: 4 (Hint: Use Problem 2 iii).) iii) Suppose C is a 2 x 2 matrix with tr (C) = 5 and det(C) = 6. Find the eigenvalues of C. (Hint: find the characteristic polynomial fc(1).)

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