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Unformatted text preview: −9 E= 0
from Exercise 1 above is an upper triangular matrix whereas
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
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?
34 and B = 0 −3
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
−47 −2 1. (a) 7B − 4A =
(b) AB = −10
−20 −1 (c) BA = (h)...
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