The big question is how did we know to use 41 we need

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: −9 E= 0 0 0 −5 from Exercise 1 above is an upper triangular matrix whereas F= 10 30 is a lower triangular matrix. (Zeros are allowed on the main diagonal.) Discuss the following questions with your classmates. (a) Give an example of a matrix which is neither upper triangular nor lower triangular. (b) Is the product of two n × n upper triangular matrices always upper triangular? (c) Is the product of two n × n lower triangular matrices always lower triangular? (d) Given the matrix A= 12 34 write A as LU where L is a lower triangular matrix and U is an upper triangular matrix? (e) Are there any matrices which are simultaneously upper and lower triangular? 6. Let A= 12 34 and B = 0 −3 −5 2 Compare (A + B )2 to A2 + 2AB + B 2 . Discuss with your classmates what constraints must be placed on two arbitrary matrices A and B so that both (A + B )2 and A2 + 2AB + B 2 exist. When will (A + B )2 = A2 + 2AB + B 2 ? In general, what is the correct formula for (A + B )2 ? 492 Systems of Equations and Matrices 8.3.2 Answers −4 −29 −47 −2 1. (a) 7B − 4A = (b) AB = −10 1 −20 −1 (c) BA = (h)...
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