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in the matrix forms and . Then use these to obtain a direct relationship
between Z and X.
(b) Use the equation obtained in (a) to express and in terms of , , and .
(c) Check the result in (b) by directly substituting the equations for , , and into the equations for and
and then simplifying.
If A is and B is , how many multiplication operations and how many addition operations are needed to
13. calculate the matrix product ?
Let A be a square matrix. if .
14.
(a) Show that
(b) Show that if .
Find values of a, b, and c such that the graph of the polynomial passes through the points (1, 2),
15. (−1, 6), and (2, 3).
16. (For Readers Who Have Studied Calculus) Find values of a, b, and c such that the graph of the polynomial
passes through the point (−1, 0) and has a horizontal tangent at (2, −9).
Let be the matrix each of whose entries is 1. Show that if , then
17.
Show that if a square matrix A satisfies , then so does .
18.
Prove: If B is invertible, then if and only if .
19.
Prove: If A is invertible, then and are both invertible or both not invertible.
20.
Prove that if A and B are matrices, then
21.
(a)
(b)
