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(c)
(d)
Use Exercise 21 to show that there are no square matrices A and B such that
22.
Prove: If A is an matrix and B is the matrix each of whose entries is , then
23.
where is the average of the entries in the ith row of A.
24. (For Readers Who Have Studied Calculus) If the entries of the matrix
are differentiable functions of x, then we define
Show that if the entries in A and B are differentiable functions of x and the sizes of the
matrices are such that the stated operations can be performed, then
(a)
(b)
(c)
25. (For Readers Who Have Studied Calculus) Use part (c) of Exercise 24 to show that
State all the assumptions you make in obtaining this formula.
