Page 179 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let A be an matrix and B the matrix that results when the rows of A are written in reverse order (last row becomes
12. the first, and so forth). How are and related?

Indicate how will be affected if
13.

(a) the ith and th rows of A are interchanged.

(b) the ith row of A is multiplied by a nonzero scalar, .

(c) times the ith row of A is added to the th row.

Let A be an matrix. Suppose that is obtained by adding the same number to each entry in the ith row of A and

14. that is obtained by subtracting from each entry in the ith row of . Show that .

Let
15.

(a) Express as a polynomial .

(b) Express the coefficients and in terms of determinants and traces.

Without directly evaluating the determinant, show that
16.

Use the fact that 21,375, 38,798, 34,162, 40,223, and 79,154 are all divisible by 19 to show that
17.

is divisible by 19 without directly evaluating the determinant.

Find the eigenvalues and corresponding eigenvectors for each of the following systems.
18.

(a)