Page 760 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 760
Use the result in Exercise 15 to prove that a product of finitely many upper triangular matrices is upper triangular.
16.
Prove: If A is any matrix, then A can be factored as , where L is lower triangular, U is upper triangular,
17. and P can be obtained by interchanging the rows of appropriately.
Hint Let U be a row-echelon form of A, and let all row interchanges required in the reduction of A to U be performed
first.
Factor
18.
as , where P is a permutation matrix obtained from by interchanging rows appropriately, L is lower
triangular, and U is upper triangular.
Show that if , then may be solved by a two-step process similar to the process in Example 1. Use this
19. method to solve
, where A is the matrix in Exercise 18 and .
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