Stitz-Zeager_College_Algebra_e-book

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

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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)...
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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.

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