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HW5 - EEL3105 Fall2011 Homework5 Forgradingandcredit 1...

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EEL 3105 Fall 2011 Homework 5 For grading and credit: 1. Consider matrices 1 3 1 2 6 2 1 3 1 2 4 6 1 3 5 3 5 8 A B (i) Calculate AB, BA, and AB BA. Find trace of AB, BA, and AB BA. What can you say about traces? (ii) Now suppose A and B are any two nxn matrices. Show that the trace of AB BA is zero. (iii) Now suppose A and B are two rectangular matrices such that both AB and BA are well defined. Show that trace(AB)=trace(BA). Can you write a formula for the trace(AB)? How does this formula relate to scalar product of vectors? 2. For matrices A and B in Problem 1, calculate determinants of A, B, AB, and BA. Which of these matrices is invertible? Give an explanation for your answers. Calculate the inverse of the matrix which is invertible. Use MATLAB (or an alternate computational math package) to check your answers.
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