Page 173 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

determinant directly would involve computing signed elementary products, and a determinant would require the

computation of signed elementary products. Even the fastest of digital computers cannot handle the computation

of a determinant by this method in a practical amount of time.

Exercise Set 2.4

Click here for Just Ask!

Find the number of inversions in each of the following permutations of {1, 2, 3, 4, 5}.
1.

(a) (4 1 3 5 2)

(b) (5 3 4 2 1)

(c) (3 2 5 4 1)

(d) (5 4 3 2 1)

(e) (1 2 3 4 5)

(f) (1 4 2 3 5)

Classify each of the permutations in Exercise 1 as even or odd.
2.
In Exercises 3–12 evaluate the determinant using the method of this section.
3.

4.

5.

6.

7.