EEL 3105Fall 2011Homework 5For grading and credit:1.Consider matrices131262131246135358AB(i)Calculate AB, BA, and AB‐BA. Find trace of AB, BA, and AB‐BA. What can you say abouttraces?(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 welldefined. Show that trace(AB)=trace(BA). Can you write a formula for the trace(AB)? Howdoes 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 thesematrices is invertible? Give an explanation for your answers. Calculate the inverse of the matrixwhich is invertible. Use MATLAB (or an alternate computational math package) to check youranswers.
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alternate computational math, computational math package