oblem 3 Consider the following 5 statements 2 of the statements are false in general Determine which 2 statements are false by

Question

oblem 3 Consider the following 5 statements 2 of the statements are false in general Determine which 2 statements are false by testing out each statement on an appropriate matrix like we did with the properties of determinants in Section 3 3 of the tutorial file Note You should not use a magic or pascal matrix for i or ii below because they have special properties not shared by other matrices Try using rand instead 1 i If A is nxn then A and A have the same eigenvalues ii If A is n xn then A and A have the same eigenvectors iii If A is n n then det Ak det A k iv If I is the nx n identity matrix and J is an nxn matrix consisting entirely of ones then the matrix I is invertible and 1 1 J J n 1 n 1 v If I is the nxn identity matrix and J is an n x n matrix consisting entirely of ones then the matrix A I is idempotent i e A A J n 1 Don t forget that you are selecting which statements are false you are not selecting which statements are true A i and iv B iv and v C iii and v D ii and iv E iii and iv F i and v G ii and v H i and ii

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