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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 Fall '10
 boykins
 alternate computational math, computational math package

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