Stitz-Zeager_College_Algebra_e-book

# Here 2 y 0 so y sin 1 and since x y 3 x cos

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lower triangular, so is A11 and, as such, the induction hypothesis applies to A11 . In other words, det (A11 ) is the product of the entries along A11 ’s main diagonal. Now, the entries on the main diagonal of A11 are the entries a22 , a33 , . . . , a(k+1)(k+1) from the main diagonal of A. Hence, det(A) = a11 det (A11 ) = a11 a22 a33 · · · a(k+1)(k+1) = a11 a22 a33 · · · a(k+1)(k+1) We have det(A) is the product of the entries along its main diagonal. This shows P (k + 1) is true, and, hence, by induction, the result holds for all n × n upper triangular matrices. The n × n identity matrix In is a lower triangular matrix whose main diagonal consists of all 1’s. Hence, det (In ) = 1, as required. 9.4 The Binomial Theorem 9.4 581 The Binomial Theorem In this section, we aim to prove the celebrated Binomial Theorem. Simply stated, the Binomial Theorem is a formula for the expansion of quantities (a + b)n for natural numbers n. In Elementary and Intermediate Algebra, you should have seen speciﬁc...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online