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Problem #5: Let A and B be n x n matrices. Which of the following statements are always true? (i) If det(A) = det(B) then det(A B) =0. (ii) If A and B are symmetric, then the matrix AB is also symmetric. (iii) If A and B are skew-symmetric, then the matrix A7 + B is also skew-symmetric. (A) none of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (iii) only (E) all of them (F) (ii) only (G) (i) only (H) (ii) and (iii) only Problem #5: | Just Save ' ' Submit Problem #5 for Grading Problem #5 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Find the eigenvalues of the following matrix. 4 -6 4 A=|0 -5 0 2 -6 -2 Problem #6: I:I separate your answers with a comma | Just Save ' ' Submit Problem #6 for Grading Problem #6 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #7: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. -7 -8 -8 2 A= | * * * | x=|-6 * * *# -8 Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue? | Just Save ' ' Submit Problem #7 for Grading Problem #7 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark