Page 56 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) Show that the product can be expressed as a linear combination of the row matrices of A with the scalar
coefficients coming from y.

(b) Relate this to the method of Example 8.

Hint Use the transpose operation.

Let A and B be the matrices in Exercise 7.
10.

(a) Use the result in Exercise 9 to express each row matrix of as a linear combination of the row matrices of B.

(b) Use the result in Exercise 9 to express each row matrix of as a linear combination of the row matrices of A.

Let C, D, and E be the matrices in Exercise 3. Using as few computations as possible, determine the entry in row 2 and

11. column 3 of .

12.
(a) Show that if and are both defined, then and are square matrices.

(b) Show that if A is an matrix and is defined, then B is an matrix.

In each part, find matrices A, x, and b that express the given system of linear equations as a single matrix equation
13. .

(a)

(b)

In each part, express the matrix equation as a system of linear equations.
14.