Page 749 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Use the result in Exercise 5 to show that
6.

Derive the formula .
7.

using the following steps.

(a) Show that

(b) Show that

(c) Apply (a) to each term on the left side of (b) to show that

(d) Solve the equation in (c) for , use the result of Exercise 5, and then simplify.

Use the result in Exercise 7 to show that
8.

Let R be a row-echelon form of an invertible matrix. Show that solving the linear system by back-substitution
9. requires

Show that to reduce an invertible matrix to by the text method requires
10.

Note Assume that no row interchanges are required.

Consider the variation of Gauss–Jordan elimination in which zeros are introduced above and below a leading 1 as soon as it is

11. obtained, and let A be an invertible matrix. Show that to solve a linear system using this version of Gauss–Jordan

elimination requires

Note Assume that no row interchanges are required. , where , then
(For Readers Who Have Studied Calculus) Show that if
12. for large values of x.

This result justifies the approximation