HOMEWORK: MATRIX OPERATIONS

A short quiz based on these problems will be held in Altgeld 245 at 1pm on
Monday February 16.

(1) Define the three matrices A,B,C as follows:

Which of the following operations make sense? If they make sense, what is
the result?
(a) A − 2B
(b) AB
(c) 2BA
(d) A + B
(e) A + CB.

(2) Do the following pair of matrices commute?

(3) True or false: The sum of two diagonal matrices of the same size is a
diagonal matrix. What about their product ?

(4) Find all matrices which commute with the matrix
What about when a = b?

(5) True or false: If A and B are the same size square matrices , then (A+B)^2 =
A^2 + 2AB + B^2.

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