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Problem_Set2

# Problem_Set2 - EEL3105 Fall2011 ProblemSet2 1...

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EEL 3105 Fall 2011 Problem Set 2 1. Consider the vector [1 2.8 3 3.33] v Find vv T . Is it symmetric? Find its eigenvalues. Is it invertible? 2. Let v be an nx1 vector. Find eigenvalues of vv T . For choices of v is vv T invertible? 3. Let A and B be two square nxn matrices. Find a formula for (A+B) 2 . 4. Suppose AB=BA. Find a formula for (A+B) n . What will happen if A and B do not commute? 5. Suppose the characteristic polynomial of a 3x3 matrix A is 3 2 4 5 3 s s s Find the characteristic polynomial of I+A where I is a 3x3 identity matrix. 6. Suppose A is an nxn matrix with characteristic polynomial 1 2 1 2 1 0 n n n n n s s s s Find the characteristic polynomial of I+A where I is an nxn identity matrix. 7. Let A and B be two matrices such that A is nxm and B is mxn. Is AB+B T A T is a symmetric matrix? Please justify your answer. 8. Let A be a symmetric matrix. Suppose 1+jb is an eigenvalue of A. Find b.

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Problem_Set2 - EEL3105 Fall2011 ProblemSet2 1...

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