Purchase Solution

Determinants, Cofactors and Permutations

Not what you're looking for?

Ask Custom Question

Q1.
Suppose An is the n by n tridiagonal matrix with 1's everywhere on the three diagonals...

Let Dn be the determinant of An; we want to find it.
(a) Expand in cofactors along the first row of An to show that Dn = Dn-1 - Dn-2

(b) Starting from D1 = 1 and D2 = 0 find D3, D4, ..., D8. By noticing how these numbers cycle around (with what period?) find D1000.

Q2.
Suppose the permutation S takes (1,2,3,4,5) to (5,4,3,2,1).
(a) What does S2 do to (1,2,3,4,5)?

(b) What does S-1 do to (1,2,3,4,5)?

Please see attached for full question.

Gilbert Strang's Linear Algebra and its Applications, 3rd edition.

Attachments
Purchase this Solution

Solution Summary

Determinants, cofactors and permutations are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Question #1
a) It is easy to know that , . Now we consider . We know that for the matrix , , has the following form
...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.